As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,;eta,;varphi)$ with the pseudo-parallel structure operator $h(=1/2Lxivarphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $Lxi$ denote the Lie derivative in the characteristic direction $xi$.