In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistribution are given. On the non-uniform grid of the uniformly distributed arc-length monitor function, the solution of the simple upwind scheme is obtained. It is proved that the adaptive simple upwind scheme based on the principle of equidistribution has uniform convergence for small perturbation parameters. Numerical experiments are carried out and the error analysis are confirmed.