The pion condensation and chiral phase transition are studied within the linear sigma model with constituent quarks (LSMq). In the chirallimit the pion condensation is always the firstorder phase transition and the phase diagrams of the pion condensate are established respectively in the (u, T), (ui, T) and (ui, u) -planes, here T, u and ui are temperature, baryon chemical and isospin chemical potentials. In the physical world, where the chiral symmetry is explicitly broken the authors investigate systematically the phase structure of pion and chiral condensates in the (T-u-ui )space. The obtained results are mainly compared to the existing data derived from the lattice QCD (LQCD) and the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model.