Hydraulic calculations of complex pipe networks are generally solved by professional software. This study investigates the process of recursively modeling complex pipe networks and solving their hydraulic calculations based on a recursive algorithm. An algorithm of oscillatory convergence and alternately driving recursion is proposed to address the multi-path recursive states arising from multi-inlet complex pipe networks, whose calculation results fully comply with the requirements for pipeline calculations in engineering fluid mechanics. The calculation program developed according to this algorithm enables one-click import of the pipe network models and directly calculate the flow rates and the pressure distribution of the pipe network. The program code is highly encapsulated and portable. In the final section, the fire-fighting system of a domestic luxury cruise ship is analyzed. The program directly calculates the flow rates and the pressure distribution after simplified modeling, determines the fire-pump parameters, and identifies the critical locations of the pipe network, which provides guidance for the design. The results show that the proposed algorithm and program can calculate complex pipe networks. It can provide a calculation reference for the design of complex pipe networks and even the determination of the principal parameters of the system.