A high-strength hot-rolled steel sheet consisting of: in mass%, C: 0.02% to 0.1%; Si: 0.001% to 3.0%; Mn: 0.5% to 3.0%; P: 0.1% or less; S: 0.01% or less; Al: 0.001% to 2.0%; N: 0.02% or less; Ti: 0.03% to 0.3%; and Nb: 0.001% to 0.06%, at least one element selected from the group consisting of: Cu: 0.001 to 1.0%; Cr: 0.001 to 1.0%; Mo: 0.001 to 1.0%; Ni: 0.001 to 1.0%; V: 0.01 to 0.2%; and the steel sheet further optionally containing B: 0.0001% to 0.005%; and 1% or less of Zr, Sn, Co, W and Mg in total, and the balance being composed of Fe and inevitable impurities, a parameter Q expressed by Mathematical expression 1 below being 30.0 or more, a microstructure being made of a ferrite structure, a bainite structure, or a structure mixed with the ferrite structure and the bainite structure, an average grain size of grains included in the microstructure being 6 μm or less, an X-ray random intensity ratio of plane on a rolled surface being 2.4 or less, and on a cross section with a sheet width direction set as a normal line, with regard to inclusions having a major diameter of 3.0 μm or more, a maximum of a major diameter/minor diameter ratio expressed by (a major diameter of the inclusion)/(a minor diameter of the inclusion) being 8.0 or less, a sum total of a rolling direction length per 1 mm 2 cross section of a predetermined inclusion group composed of plural inclusions each having a major diameter of 3.0 μm or more and a predetermined extended inclusion having a length in a rolling direction of 30 μm or more being 0.25 mm or less, the plural inclusions composing the predetermined inclusion group congregating in both the rolling direction and a direction perpendicular to the rolling direction 50 μm or less apart from each other, and the predetermined extended inclusion being spaced over 50 μm apart from all the inclusions each having a major diameter of 3.0 μm or more in at least either the rolling direction or the direction perpendicular to the rolling direction, Q = Ti 48 / S 32 wherein [Ti] indicates the Ti content (mass%) and indicates the S content (mass%). in mass%, C: 0.02% to 0.1%; Si: 0.001% to 3.0%; Mn: 0.5% to 3.0%; P: 0.1% or less; S: 0.01% or less; Al: 0.001% to 2.0%; N: 0.02% or less; Ti: 0.03% to 0.3%; and Nb: 0.001% to 0.06%, Cu: 0.001 to 1.0%; Cr: 0.001 to 1.0%; Mo: 0.001 to 1.0%; Ni: 0.001 to 1.0%; V: 0.01 to 0.2%; and the steel sheet further optionally containing B: 0.0001% to 0.005%; and 1% or less of Zr, Sn, Co, W and Mg in total, and the balance being composed of Fe and inevitable impurities, a parameter Q expressed by Mathematical expression 1 below being 30.0 or more, a microstructure being made of a ferrite structure, a bainite structure, or a structure mixed with the ferrite structure and the bainite structure, an average grain size of grains included in the microstructure being 6 μm or less, an X-ray random intensity ratio of plane on a rolled surface being 2.4 or less, and on a cross section with a sheet width direction set as a normal line, with regard to inclusions having a major diameter of 3.0 μm or more, a maximum of a major diameter/minor diameter ratio expressed by (a major diameter of the inclusion)/(a minor diameter of the inclusion) being 8.0 or less, a sum total of a rolling direction length per 1 mm 2 cross section of a predetermined inclusion group composed of plural inclusions each having a major diameter of 3.0 μm or more and a predetermined extended inclusion having a length in a rolling direction of 30 μm or more being 0.25 mm or less, the plural inclusions composing the predetermined inclusion group congregating in both the rolling direction and a direction perpendicular to the rolling direction 50 μm or less apart from each other, and the predetermined extended inclusion being spaced over 50 μm apart from all the inclusions each having a major diameter of 3.0 μm or more in at least either the rolling direction or the direction perpendicular to the rolling direction, Q = Ti 48 / S 32 wherein [Ti] indicates the Ti content (mass%) and indicates the S content (mass%).