The analysis of thermoluminescence (TL) glow curve is an important way to investigate the trap structure of the materials as well as the kinetics of the charge carrier transfer. Most currently used methods rely on the existence of an explicit expression of the theoretical glow curve. However, since the set of kinetic equations describing the TL process does not have analytical solutions, the derivation of an explicit expression always involves some sort of assumptions and approximations, which can compromise the universality and accuracy of the method. This paper proposes a new algorithm that focuses on the original kinetic equations and does not necessitate an explicit expression to analyze the TL glow curve. This algorithm establishes an objective function to evaluate the fitness of a selected combination of kinetic parameters, and then using the genetic algorithm (GA) to search for the optimal parameters. Various occasions were numerically simulated, demonstrating the algorithm's capability to handle kinetics of different order, multiple interactive peaks, deep trap, non-linear heating, and temperature dependent parameter cases. An actual glow curve of the LiF:Mg,Cu,P chip was also analyzed using this algorithm, and the corresponding kinetic parameters were identified. This algorithm provides a more universal and valid method for TL glow curve analysis.