La(Fe, Si) ₁₃-based alloys have attracted more and more attention, for they exhibit giant magnetocaloric effects. In order to broaden their magnetic refrigeration temperatureranges, achieving a series of La(Fe, Si) ₁₃-based alloys with different magnetic phase transition temperatures is of great significance. Unlike the traditional research method, in this paper, a high-throughput first-principles computation is performed to estimate the magnetic phase transition temperature of the LaFe _11.5Si _1.5-based alloy by employing AMS-BAND software and the mean field theory. We investigate the effects of doping Mn, Co, Ni, Al atoms and Fe-vacancies on the magnetic phase transition temperature of LaFe _11.5Si _1.5-based alloy, and give the phase diagrams between the composition and magnetic phase transition temperature. The calculated results demonstrate that the magnetic phase transition temperature of the LaFe _11.5Si _1.5-based alloy increases with the increase of Co and Ni content. However, it shows an opposite result when Mn atom is doped. As for the LaFe _11.5Si _1.5-based alloy with the Fe-vacancies, the research results indicate that the absence of Fe atoms will reduce the magnetic phase transition temperature. Furthermore, when Mn, Co, Ni and Al atoms are doped in the alloys with Fe-vacancies, the variation tendency of the magnetic phase transition temperature with the change of the doping content is similar to that without the Fe-vacancies. Some estimated results are compared with the experimental or reported results, showing that they are in good agreement with each other. The PDOS and the magnetic moments of Fe atoms in the Mn, Co, Ni, Al-doped LaFe _11.5Si _1.5-based alloys are calculated, in which only the doping of Mn atoms can increase the magnetic moments of Fe atoms. Using the method of high-throughput first-principles calculation can effectively reduce the research cost and improve the working efficiency. In addition, it can provide technical support for the experimental selection of magnetocaloric materials with appropriate magnetic phase transition temperatures.