In this paper, a joint two dimensional (2D) direction of departure (DOD) and 2D direction of arrival (DOA) estimation strictly noncircular (NC) ESPRIT algorithm for the L-shaped bistatic multiple input multiple output (MIMO) radar is proposed. In the case of the incident signals are NC signals, we first utilize the received data vector and its conjugate counterparts to construct a new data vector, and then the ESPRIT method is adopted to estimate the 2D-DODs and 2D-DOAs by joint diagonalization of the NC-based direction matrices, which can automatically pair the four dimensional (4D) angle parameters. Simulation results are included to verify the effectiveness of the proposed algorithm.