We present a scheme for engineering the extended two-component Bose-Hubbard model using polariton condensate supported by an optical microcavity. Compared to the usual two-component Bose-Hubbard model with only Kerr nonlinearity, our model includes a nonlinear tunneling term which depends on the number difference of the particle in the two modes. In the mean-field treatment, this model is an analog to a nonrigid pendulum with a variable pendulum length whose sign can be also changed. We study the dynamic and groundstate properties of this model and show that there exists a first-order phase transition as the strength of the nonlinear tunneling rate is varied. Furthermore, we propose a scheme to obtain the polariton condensate wave function.