We demonstrate a laser frequency drift measurement system based on the delayed self-heterodyne technique. To ensure long-term measurement validity, an ultra-stable optical fiber delay line is realized by monitoring and locking the transmission delay of a probe signal with a well-designed phase-locked loop. The frequency stability indicated by overlapping Allan deviation is 6.39 × 10−18 at 1000-s averaging time, ensuring a real-time measurement resolution of 18.6 kHz. After carefully determining the optimal fiber length, a 5-kHz periodic frequency change with a period of merely 0.5 s is easily detected, proving its high frequency resolution and fast response. At last, the frequency drift characteristics of three different lasers after being powered on are investigated. Thanks to its high precision and long-term stability, the proposed method is ideal for monitoring long-term laser frequency evolution with high precision.