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 （23.8 kHz） 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.