A general contact model for a lap joint interface based on non-Gaussian surfaces was proposed. The effect of surface topography parameters on microslip behavior in a lap joint interface was studied. Pearson system was applied to produce non-Gaussian surfaces. Combining the topographical-dependent Zhao–Maietta–Chang (ZMC) model with the physical-related Iwan model, the nonlinear constitutive relationship of a lap interface was constructed by using Masing hypothesis. Meanwhile, the probability density function of asperity heights of an infinitely smooth surface was mathematically proved to be a delta function, verifying that the calculated value of friction in the model conforms to the physical law. Gauss-Legendre quadrature was conducted to calculate contact relations of different Pearson distribution surfaces. Furthermore, numerical results of microslip loops under oscillating tangential forces were compared with the published experiments, indicating the present model considering non-Gaussian surfaces could agree well with the experiments.