In this paper, we consider a multi-input-multi-output (MIMO) wiretap channel with a multi-antenna eavesdropper, where a private cooperative jammer is employed to improve the achievable secrecy rate. The legitimate user pays the legitimate transmitter for its secured communication based on the achieved secrecy rate. We first approximate the legitimate transmitter covariance matrix by employing Taylor series expansion, then this secrecy rate problem can be formulated into a Stackelberg game based on a fixed covariance matrix of the transmitter, where the transmitter and the jammer try to maximize their revenues. This secrecy rate maximization problem is formulated into a Stackelberg game where the jammer and the transmitter are the leader and follower of the game, respectively. For the proposed game, Stackelberg equilibrium is analytically derived. Simulation results are provided to show that the revenue functions of the legitimate user and the jammer are concave functions and the Stackelberg equilibrium solution has been validated.