Highly matched and precisely locked to the absorption lines of rubidium (Rb) atoms, 780 nm lasers play a crucial role in fields such as quantum computing, precision measurements, and high-sensitivity sensing, with clear requirements for strong coherence and fast tunability. In this paper, based on the self-injection locking and ultra-high quality factor Whispering gallery mode (WGM) cavity, a 780 nm narrow linewidth (23.8kHz) tunable laser with a single longitudinal mode output is verified. More importantly, benefiting from the optimized combined coupling coefficient K and via the lithium niobate electro-optic effect, the laser frequency detuning is effectively improved, with the experimental tuning range reaching 110 pm and the tuning efficiency of 6.4 pm/V. This work provides a high-performance design solution for fast-tunable narrow-linewidth lasers for applications in the near-infrared range, which is expected to play an essential role in the future.