We report an all-solid-state near-infrared single-frequency (single longitudinal mode, SLM) Pr3+:LiYF4 (Pr:YLF) laser with the spectral linewidth at the sub-picometer level. The SLM lasers with center wavelengths of 868 and 907 nm are realized in Pr:YLF crystal for the first time to the best of our knowledge. The maximum output powers of SLM lasers at 868 and 907 nm are 102 and 213mW, corresponding to the narrowest spectral linewidths of 82 MHz (0.21 pm) and 94 MHz (0.26 pm), respectively. At the maximum output power, the beam quality factors in the x and y directions are measured as 1.25 and 1.16 at 868 nm and 1.21 and 1.13 at 907 nm, respectively. The output power stabilities of the 868 and 907 nm SLM lasers are calculated as 1.39% and 0.87%, respectively. The successful realization of 868 and 907 nm all-solid-state SLM lasers makes up for the gap that the Pr:YLF SLM lasers developed in the past are focused on the visible region, enriches the types of near-infrared (NIR) SLM lasers, and can provide practical applications in biomedicine, cold atom physics, and optical atom manipulation.