The all optical AND logical operation using the wavelength conversion in the fiber optical parametric amplifier (FOPA) is completed. The logical relation between idler output and two input optical waves in the FOPA is proved through the principle of wavelength conversion and the phase match condition for four types of code word in two input optical waves. By solving nonlinear coupled equations numerically utilizing Runge-Kutta method, the all optical AND logical relation between output and two input optical waves in the FOPA is verified numerically, then the output power of idler in this all optical AND logic gate influenced by fiber length, the power ratio of two input optical waves and the values of two input wavelengths is investigated. These results are conducive to the optimized design of all optical AND logic gate in practice. The selection for the width of input optical pulse in 100Gbit/s all optical AND logical operation is discussed.