Recently, directional sensor networks (DSN) have received a great deal of attention due to their wide range of applications. Unlike conventional omni-directional sensors that always have an omni-angle of sensing range, a DSN is composed of many directional sensors which have a limited angle of sensing range due to technical constraints or cost considerations. This paper studies coverage prediction and number estimation model for directional sensor networks. Aiming at better guiding initial deployment of DSN, a novel probability-based networks coverage prediction model with the boundary effects named PCPMB is proposed. Simulation results show that the proposed model outperforms the previous published model without boundary effect.