In this work, we consider the dynamics of KP tumor model [12]. First, the non-negativity of solutions are showed and sufficient conditions to guarantee the unboundedness and boundedness of solution are established, respectively. Then we present the explicit form of tumor-free equilibrium with or without treatment. By applying local analysis to the linearized system, local stability of the tumor free equilibrium are verified. Moreover, a global dynamical result is also investigated. Next, we find the sufficient condition of the existence of positive equilibria. Unfortunately, there maybe have other positive equilibria. Finally, some biological implications and numerical simulations are presented in the last section.