By using exact wave functions of an electron in a terahertz laser field, we calculated the electron resonant tunneling through a double barrier structure. It is found that the laser field has two effects on the current voltage characteristics. First, it introduces additional tunneling states through the structure due to multiple photon processes (emission, absorption, scattering). Second, it reduces the width of the bistable region. At high field strength and low frequencies, the bistability can be completely removed. This can provide a method by which to tune the bistable region in a double barrier structure.