Leland model is a nonlinear option pricing equation in which the transaction cost was taken into account based on the Black Schole model. An adaptive wavelet homotopy perturbation method based on interpolation wavelet function for nonlinear PDEs is proposed. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix differential equations; Next, the homotopy perturbation method is developd to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method to solve nonlinear differential equations. Third, the exact analytical solution of the system of constant coefficient and nonhomogeneous differential equations is deduced by this method, which is simpler than traditional methods. At last, the Leland model is taken as an example to test this new method. The numerical result shows that this method possesses many merits such as higher numerical stability and high precision.