A beam homogenizer comprising: a first optical element (303a, 303b) for forming a first laser beam by dividing a spot of a laser beam from a light source in a short-side direction of a rectangular shape; a second optical element for forming a second laser beam by dividing a spot of the first laser beam in a long-side direction of the rectangular shape, wherein the second optical element is an off-axis lens array; a third optical element for forming a third laser beam by converging a spot of the second laser beam in the long-side direction; and a fourth optical element for forming a fourth laser beam that is emitted to an irradiation surface by converging a spot of the third laser beam in the short-side direction, wherein the irradiation surface is conjugated through the third optical element with a hypothetical plane where the divided laser beams are superposed when the second laser beam is extended to a side of the light source, wherein the off-axis lens array comprises: a plurality of off-axis cylindrical lenses extending in the direction of the cylinder axis and having a width in the direction perpendicular thereto; wherein each off-axis cylindrical lens has a curved surface portion at the side receiving the first laser beam and a plane surface portion at the side opposed thereto; wherein for each off-axis cylindrical lens a center axis is perpendicular to the plane surface portion and centered with respect to the width, wherein each off-axis cylindrical lens is asymmetric in that a generating line which is located at a curved portion of the cylindrical lens that is the farthest from a plane portion of the cylindrical lens and parallel to the center axis, is for each of the off-axis cylindrical lenses spaced by a distance from the center axis thereof in an opposite direction away from a center of the lens array, wherein the distance between the generating line and the center axis of the off-axis cylindrical lenses increases from the center of the lens array toward opposite ends of the lens array. a first optical element (303a, 303b) for forming a first laser beam by dividing a spot of a laser beam from a light source in a short-side direction of a rectangular shape; a second optical element for forming a second laser beam by dividing a spot of the first laser beam in a long-side direction of the rectangular shape, wherein the second optical element is an off-axis lens array; a third optical element for forming a third laser beam by converging a spot of the second laser beam in the long-side direction; and a fourth optical element for forming a fourth laser beam that is emitted to an irradiation surface by converging a spot of the third laser beam in the short-side direction, wherein the irradiation surface is conjugated through the third optical element with a hypothetical plane where the divided laser beams are superposed when the second laser beam is extended to a side of the light source, wherein the off-axis lens array comprises: a plurality of off-axis cylindrical lenses extending in the direction of the cylinder axis and having a width in the direction perpendicular thereto; wherein each off-axis cylindrical lens has a curved surface portion at the side receiving the first laser beam and a plane surface portion at the side opposed thereto; wherein for each off-axis cylindrical lens a center axis is perpendicular to the plane surface portion and centered with respect to the width, wherein each off-axis cylindrical lens is asymmetric in that a generating line which is located at a curved portion of the cylindrical lens that is the farthest from a plane portion of the cylindrical lens and parallel to the center axis, is for each of the off-axis cylindrical lenses spaced by a distance from the center axis thereof in an opposite direction away from a center of the lens array, wherein the distance between the generating line and the center axis of the off-axis cylindrical lenses increases from the center of the lens array toward opposite ends of the lens array. a plurality of off-axis cylindrical lenses extending in the direction of the cylinder axis and having a width in the direction perpendicular thereto; wherein each off-axis cylindrical lens has a curved surface portion at the side receiving the first laser beam and a plane surface portion at the side opposed thereto; wherein for each off-axis cylindrical lens a center axis is perpendicular to the plane surface portion and centered with respect to the width, wherein each off-axis cylindrical lens is asymmetric in that a generating line which is located at a curved portion of the cylindrical lens that is the farthest from a plane portion of the cylindrical lens and parallel to the center axis, is for each of the off-axis cylindrical lenses spaced by a distance from the center axis thereof in an opposite direction away from a center of the lens array, wherein the distance between the generating line and the center axis of the off-axis cylindrical lenses increases from the center of the lens array toward opposite ends of the lens array.