To solve the difficult problem of selecting initial guess values for component-level aero-engine start-up models, a novel method based on the flow-based back-calculation algorithm (FBBCA) is investigated. By exploiting the monotonic feature of low-speed aero-engine component characteristics and the principle of flow balance abided by components in the start-up process, this method traverses all the flows in each component characteristic at a given engine rotor speed. This method also limits the pressure ratios and flow rates of each component, along with the surplus power of the high-pressure rotor. Finally, a set of “fake initial values” for iterative calculation of the aero-engine start-up model can be generated and approximate true initial guess values that meet the accuracy requirement according to the Newton–Raphson iteration method. Extensive simulation verifies the low computational cost and high computational accuracy of this method as a solver for the initial guess values of the aero-engine start-up model.