Improving sensitivity is critical for the higher-order harmonic fiber Bragg grating sensors. To this aim, in this work, we have successfully introduced the phase-shift into the third harmonic fiber Bragg grating for tailoring a double-dip spectrum with a high finesse notch. The dual dips showed reversed responses for the intensity regarding the change of the temperature or axial strain, enabling a highly sensitive measuring regime using the intensity contrast between the two dips. Deduced from the sinusoidal responding curves, the highest temperature and the axial strain sensitivity could reach 0.964 dB/°C, and 0.0257 dB/μ ε, three-fold times the other intensity-based fiber sensors. This work may promote the higher-order harmonic gratings into applications for enriching wavelength utilization.