Tunable diode laser absorption spectroscopy is widely used for temperature measurement in combustion monitoring due to its merits of rapidity, non-contact capability, and high precision. In actual applications, the beam-steering effect will cause time-varying distortion in the laser intensity signal, resulting in a low signal-to-noise ratio and inaccurate extraction of the absorption spectrum. This work proposes a cost-effective distortion detection scheme and adaptive distortion filter and compensation algorithm for the extraction of the beam-steering effect immune laser absorption spectrum. Turbulent flame monitoring experiment results prove the proposed method can improve the signal-to-noise ratio of the raw transmitted absorptive laser signal by 35 dB after the beam-steering distortion has been compensated. When compared with the temperature results calculated from the distorted absorptive laser signal, the results from the distortion-compensated absorptive laser signal show a significant improvement in both robustness and precision. The experimental results demonstrate that the successful temperature fitting rate has increased from 93.7 % to 100 % (over 1000 repetitions), and the average standard deviations of temperature have decreased from 296.6 K to 61.8 K. The proposed method is cost-effective and compact, which will potentially play an important role in dynamic combustion monitoring and diagnosis.