A highly reliable and stable erbium-doped mode-locked fiber laser was constructed using a 45°-tilted fiber grating (45°-TFG) as a fiber polarizer. Based on this, precise signal stabilization of the repetition frequency frep and carrier-envelope offset frequency fceo was achieved. When the pump power is 228 mW, the mode-locked laser oscillator based on a 45°-TFG can achieve an ultra-short pulse output of 3 dB with a spectral bandwidth of 60.4 nm and a pulse width of 68 fs. The root mean square stability of the power reaches 0.033% within 12 hours, and it can maintain a good stretched mode-locked state over a large pump range. After self-built chirped pulse amplification, super-continuum spectrum generation, and f-2f self-reference beat interference optical path, fceo signal with a signal-to-noise ratio of 32 dB was obtained. Finally, by building an active feedback control circuit based on a phase-locked loop, the frep and fceo signals were traced back to a GPS time-frequency system, and the frequency instability of the frep and fceo signals was measured to be 2.38×10^-12 and 6.41×10^-16 within an average time of 1 second. This is the first implementation of a fiber laser frequency comb based on a 45°-TFG, indicating the potential of a 45°-TFG based mode-locked fiber laser in practical applications.