This invention relates to one optical mode converter, which is formed by matrix optics principle and designs one optical lens of single mode converter. The lens is one integration structure made of grads refraction rate medium with column in middle and column planes with parallel lines on both ends. The optical lens is located between the input beams girdling side of Ermy to Gaussian beam with the output girdling side of Ermy to Gaussian beam. The optical system transmission matrix is Míõ and when the system satisfies certain parameters, the M equals to current converter optical system matrix M to realize the conversion from HG beam to the LG beam.