A switchable high power dual-wavelength self-similar parabolic pulse laser is proposed based on normal dispersion single-mode fiber, Yb3+ doped gain fiber and multimode fiber Bragg grating. The transmission and evolution of dual-wavelength self-similar parabolic pulse are simulated numerically by split-step Fourier method with the nonlinear Schrdinger equations. The input pulses produce self-similar parabolic pulses in normal dispersion single-mode fiber and Yb3+ doped gain fiber. The dual-wavelength selection is carried out by a multimode fiber Bragg grating for laser. The dual-wavelength stable operation is realized by adjusting the polarization controller. Numerical simulation shows that the operation of the laser is feasible and effective.