KP equation is an important integrable equation which has important applications in shallow water waves and ocean internal waves. By means of an asymptotic perturbation method, we study the initial value problem of the KP equation with initial data consisting of parts of exact line-soliton solutions of the equation.  We then perform numerical simulations of the initial value problem and show that they are in excellent agreement with the results obtained by the perturbation method. Also we study the algebro-geometric solutions with different genus which have potential important applications in periodic internal waves.