Dynamical stability plays an essential role in phase transition and structure, and it could be a fundamental method of discovering new lead-free perovskite materials. The perovskite materials are well-known for their excellent optoelectronic properties, but the lead element inside could be a hindrance to future development. This research is trying to predict the promising cation candidates in the high-temperature application for lead-free perovskite materials from the replacement of lead in MAPbCl3 (MA = methylammonium) with alkaline-earth cations. The alkaline-earth cations are of a stable positive divalent sort, which is the same as Pb, and most of them are abundant in nature. Therefore, by improving the dynamical stability, the Mg2+, Ca2+, and Sr2+ cations replacement of lead ions could stabilize the perovskite structure by decreasing the imaginary part of phonon density of states. Finally, the density functional theory results show that the MACaCl3 could be a dynamic stable lead-free methylammonium perovskite material with an ultrawide band gap (5.96 eV).