With the development of deep space exploration technology, manned missions to Mars are expected to be realized in the near future. However, the journey to Mars requires more supplies and fuel than near-Earth missions, including moon landings. Using the traditional Apollo-style mission method will result in the spacecraft reaching the LEO mass of 2000 tons, which is not easy to achieve. The use of the modular design method and multiple launches will significantly reduce the mass of a single launch. In addition, the use of nuclear power engines (Nuclear Thermal Propulsion, NTP, and Nuclear Electric Propulsion, NEP) can greatly improve propulsion efficiency, reducing the mass of the propellant. This paper uses the Mission Architecture Matrix (MAM) method to concisely and precisely analyze a series of mission architectures in the case of impulse maneuver transfer and low-thrust transfer. The results show that when only chemical propulsion (specific impulse is 440s) is used, the maximum LEO launch mass in the optimal mission architecture is 325 tons, and the total LEO mass of the system is 1142 tons. With the usage of NTP (specific impulse is 900s) and NEP (the specific impulse is 6000s) technology, the maximum LEO launch mass in the optimal mission architecture is only 85 tons, and the total LEO mass of the system is only about 400 tons. Considering the current rocket technology, the total cost is about USD 1149 million US.