An all-fiber laser using polarization-maintaining and ring-core fibers that are capable of automatically generating stable TE01 and TM01 modes is proposed and demonstrated experimentally. Two vector-mode coupling long-period fiber gratings (LPFGs) fabricated by a high-frequency CO2 laser are used in the fiber laser to realize efficient coupling between HE11 mode and TE01/TM01 mode. The polarization dependence of the LPFGs is simulated using the coupled-mode theory and verified by experiments. A ring-core fiber is employed to support the stable propagation of TE01 and TM01 modes. By carefully aligning the polarization direction of the input light, the mode coupling ratios of both LPFGs exceed 15 dB. The mode purities of TE01 and TM01 modes are 92.4% and 97.3%, respectively. Owing to the all-polarization-maintaining structure, the laser output is highly stable under environmental disturbance. This laser can be used as a stable cylindrical vector beam source for a wide range of applications, including surface plasmon excitation, optical tweezers, high-resolution metrology and so on.