In this paper, we try to provide a simple analytical approach to describe distribution of intersection entering traffics on a grid road network. The approach is a continuous model with explicit structure and free of the need of a detailed OD (Origin-Destination) table. For the purpose of proper road network planning and controls, it is very important to quantify the traffic distribution on a road network. Currently the most widely used approaches can be roughly divided into two types: the static traffic assignment models and the dynamic traffic simulation models, either macroscopic or microscopic ones. However, the traditional models demands very detailed OD information, with inevitable complicated, black-box type of algorithms. As the result, the users often reach to the outputs without knowing the underlying logic behind. The traditional models are all link oriented, except the microscopic analysis, intersections play a trivial role (if any) in the traditional models, despite the fact that intersections rather than basic sections of road links, decide the performance of urban road networks in modern cities. In this paper we assume the passing probability of an intersection equals to the utilization of the intersection in the routes between OD pairs within a road network. Under this assumption, an explicit analytical model is developed to describe the distribution of traffic within a grid network by a single pair of OD, firstly a discrete model and followed by a continuous model that can be subjected to the method of integral in the future. Finally we use a proved commercial simulation model to validate the proposed approach. Our approach can be regarded as a simplified estimation method of traffic distribution and this work is also helpful for the researches on the road network density. Through our research we do not consider about the influence of congestion since our objective is limited to the planning stage only.