This paper focuses on the problem of modeling for small world effect on complex networks. Let’s consider the supercritical Poisson continuous percolation on \(d\)-dimensional torus \(T^d_n\) with volume \(n^d\). By adding “long edges (short cuts)” randomly to the largest percolation cluster, we obtain a random graph \(\mathscr G_n\). In the present paper, we first prove that the diameter of \(\mathscr G_n\) grows at most polynomially fast in \(\ln n\) and we call it the Poisson Geometry Small World. Secondly, we prove that the random walk on \(\mathscr G_n\) possesses the rapid mixing property, namely, the random walk mixes in time at most polynomially large in \(\ln n\).