The numerical model of the linear optical amplifier (LOA) is built based on the rate equations. The gain clamping characteristics of LOA are simulated. By combining the transmission matrix of the symmetrical, Mach-Zehnder interferometer (MZI), the all-optical XOR model of LOA-MZI has been constracted, and two XOR operations are realized at 40 Gbit/s. The performance of the XOR result has been analyzed and compared with the semiconductor optical amplifier (SOA)-MZI. The result differences of the two XOR gates are explained from the structural property. The theoretical results indicate that, LOA has a flat gain characteristic and improved tolerance against small signal distortions, the carrier recovery time is shorted by the vertical laser field, and all-optical XOR functionality can been achieved by using LOA-MZI. By using the differential phase scheme the high-speed operation limitation by the carrier recovery time is solved, and better results can be achieved by choosing the delay time properly. The output signals of LOA-MZI have opener eye diagram, higher extinction ratio, lower peak chirp and lower sensitivity to wavelength.