Based on the spatial profiles and polarization states evolution process of the first-order modes resulted from stress-induced birefringence in the few-mode fiber (FMF), we analyze the mapping relationship between the input polarization states represented on polarization PS and the output spatial profiles represented on the orbital PS of the FMF with respect to the magnitude and orientation of birefringence. When the input mode lobe orientation and the phase differences between the four eigenmodes of FMF induced by the stress birefringence satisfy a given condition, the mapping relationship between the input polarization PS and the output orbital PS is linear. Thus, the arbitrary points on the orbit PS can be generated at the output of stressed FMF by controlling the polarization state of the input modes. Then we experimentally verify that, an electrical single-mode polarization controller, a mode converter for converting fundamental mode to higher-order mode, a polarization controller mounting a coil of two-mode fiber and a polarizer can be employed to generate arbitrary first-order spatial modes on the orbital PS by controlling the input single-mode polarization states. The positions on the orbital PS of the generated first-order modes, which are obtained by calculating the three normalized Stokes parameters of output modes, agree well with the simulation ones. The correlation coefficients between the theoretical mode profiles and the experimental ones are higher than 80%. Since the spatial profile evolutions depend on the variations of the input polarization states, a potential advantage of this method is high-speed switching among desired first-order modes by using the commercial devices switching the state of polarization.