On the basis of Mean Field Approximation (MFA), Monte Carlo Simulations (MCS) and ab initio calculations we have studied the phase diagrams and magnetic properties of the bulk perovskite, LaMnO3 using Ising model Hamiltonian. It is shown that the antiferromagnetic coupling between next neighbors Mn ions is reponsible for a series of magnetic phase transitions. The transition temperature and the critical exponents obtained, in the framework of Monte Carlo simulations, using the experimental values of the exchange couplings and magnetic anisotropy are in agreement with the experimental ones. The exchange couplings deduced from ab initio calculations lead, by using Monte Carlo simulations, to a quantitative agreement with the experimental transition temperatures.