A high strength hot rolled steel sheet having a thickness exceeding 4 mm and excellent fatigue resistance and a composition containing, in terms of mass%, C: 0.05 to 0.15%, Si: 0.2 to 1.2%, Mn: 1.0 to 2.0%, P: 0.03% or less, S: 0.0030% or less, Al: 0.005 to 0.10%, N: 0.006% or less, and at least one selected from Ti: 0.03 to 0.13%, Nb: 0.02 to 0.10%, and V: 0.02 to 0.15%, optionally at least one selected from Cr: 0.01 to 0.2%, Mo: 0.005 to 0.2%, Cu: 0.005 to 0.2%, and Ni: 0.005 to 0.2%, optionally B: 0.0002 to 0.003%, and optionally one or both of Ca: 0.0005 to 0.03% and REM: 0.0005 to 0.03%, the balance being Fe and unavoidable impurities, wherein a surface layer portion having a depth of 500 μm from the surface in the sheet thickness direction contains 50% or more of a bainite phase in terms of area fraction, the bainite phase having an average grain diameter of 5 μm or less; a sheet thickness center portion that extends from a position located at a depth of 1/4 of the sheet thickness to a position located at a depth of 3/4 of the sheet thickness contains 90% or more of a bainite phase in terms of area fraction, the bainite phase having an average grain diameter of 4 μm or less; a tensile strength TS is 780 MPa or more, and a 2,000,000 cycle fatigue strength of 580 MPa or more in a pull-pull-type axial tensile fatigue test at a stress amplitude of 0.05 in terms of stress ratio, wherein bainite refers to bainite and bainitic ferrite other than polygonal ferrite, pearlite, martensite, and carbides; the average grain diameter is determined by taking a test specimen from the hot rolled steel sheet; a sheet cross-section taken parallel to the rolling direction is polished and corroded with a 3% nital solution to expose the microstructure; the microstructures of the surface layer portion and the sheet thickness center portion are observed with a scanning electron microscope, magnification: 3000; five or more areas of observations are photographed and image-processed to calculate the microstructure fractions of the respective phases and the average grain diameter of the bainite phase; in the surface layer portion, a first photograph is taken at a position from which a 50 μm depth portion is removed from the outermost surface; the subsequent photographs are taken at 50 μm intervals from that position; in the sheet thickness center portion, a total of five photographs are taken respectively at five positions at depths of 2/8, 3/8, 4/8, 5/8, and 6/8 of the sheet thickness; and the average grain diameter is determined by drawing two lines perpendicularly intersecting each other, having a length of 80 mm, and being inclined 45° in the thickness direction on the photograph of the microstructure obtained, measuring the length of the intercept for each grain, and calculating the arithmetic average of the intercepts. and at least one selected from Ti: 0.03 to 0.13%, Nb: 0.02 to 0.10%, and V: 0.02 to 0.15%, optionally at least one selected from Cr: 0.01 to 0.2%, Mo: 0.005 to 0.2%, Cu: 0.005 to 0.2%, and Ni: 0.005 to 0.2%, optionally B: 0.0002 to 0.003%, and optionally one or both of Ca: 0.0005 to 0.03% and REM: 0.0005 to 0.03%, the balance being Fe and unavoidable impurities, wherein a surface layer portion having a depth of 500 μm from the surface in the sheet thickness direction contains 50% or more of a bainite phase in terms of area fraction, the bainite phase having an average grain diameter of 5 μm or less; a sheet thickness center portion that extends from a position located at a depth of 1/4 of the sheet thickness to a position located at a depth of 3/4 of the sheet thickness contains 90% or more of a bainite phase in terms of area fraction, the bainite phase having an average grain diameter of 4 μm or less; a tensile strength TS is 780 MPa or more, and a 2,000,000 cycle fatigue strength of 580 MPa or more in a pull-pull-type axial tensile fatigue test at a stress amplitude of 0.05 in terms of stress ratio, wherein bainite refers to bainite and bainitic ferrite other than polygonal ferrite, pearlite, martensite, and carbides; the average grain diameter is determined by taking a test specimen from the hot rolled steel sheet; a sheet cross-section taken parallel to the rolling direction is polished and corroded with a 3% nital solution to expose the microstructure; the microstructures of the surface layer portion and the sheet thickness center portion are observed with a scanning electron microscope, magnification: 3000; five or more areas of observations are photographed and image-processed to calculate the microstructure fractions of the respective phases and the average grain diameter of the bainite phase; in the surface layer portion, a first photograph is taken at a position from which a 50 μm depth portion is removed from the outermost surface; the subsequent photographs are taken at 50 μm intervals from that position; in the sheet thickness center portion, a total of five photographs are taken respectively at five positions at depths of 2/8, 3/8, 4/8, 5/8, and 6/8 of the sheet thickness; and the average grain diameter is determined by drawing two lines perpendicularly intersecting each other, having a length of 80 mm, and being inclined 45° in the thickness direction on the photograph of the microstructure obtained, measuring the length of the intercept for each grain, and calculating the arithmetic average of the intercepts.