A scheme to solve the Hamiltonian in the interacting boson-fermion model in terms of the SU(3)coup-ling basis is introduced,through which the effects of an odd particle on shape phase transitions(SPTs)in odd-A nuc-lei are examined by comparing the critical behaviors of some selected quantities in odd-even and even-even systems.The results indicate that the spherical to prolate(U(5)-SU(3))SPT and spherical to γ-soft(U(5)-O(6))SPT may clearly occur in the odd-even system with the SPT signatures revealed by various quantities including the excitation energies,energy ratio,B(E2)ratio,quadrupole moments,and one-particle-transfer spectroscopic intensities.In par-ticular,the results indicate that the spherical to prolate SPT in the odd-even system can even be strengthened by the effects of the odd particle with the large fluctuations of the quadrupole deformations appearing near the critical point.