In order to expand the continuous tunable range of a self-injection-locked laser frequency, the variation relationship of the injected locking phase of the Fabry-Perot (FP) microcavity during the frequency-thermal tuning process is studied. Based on the traditional frequency-thermal tuning methods, we explore the frequency and phase parameter characteristics of a self-injection locked laser. We propose an improved algorithm which adds self-injection locking phase compensation and DFB chip current compensation during frequency-thermal tuning methods. Experimental validation of this algorithm is conducted on a FP micro-cavity self-injection locked laser. The laser operates at a wavelength of 1550 nm with a 3 dB linewidth of 785 Hz, achieving frequency-thermal tuning methods of the FP micro-cavity using a pair of heating resistors. The improved algorithm is implemented within the microcontroller program of the laser's original drive control circuit. No modifications are made to the hardware components of the laser. Ultimately, a continuous frequency tuning range of 6 GHz is realized. This work provides a simple, efficient, and stable frequency-tuning solution for self-injection-locked lasers, demonstrating high practicality and promising market prospects.