Abstract: Pulsar glitch, is a rare phenomenon, and is a probe for studying the internal structure of pulsars. From February to December 2019, time-of-arrival measurements have been collected for Crab pulsar with the 40-meter radio telescope at Haoping Observatory of the National Time Service Center during pulsar timing observations. These measurements are analyzed by "timing solutions" with TEMPO2 fitting program. We have observed a glitch in the Crab pulsar. The glitch occurred around July 23, 2019 (MJD 58687) when Crab pulsar underwent an increase in the rotation rate of Δv_g=5.33(4)×10^-7 Hz, corresponding to fractional size of Δv_g/v=17.9(1)×10^-9. This event was followed by an exponential recovery process with a degree of recovery Q~0.88. The monitoring program of the Crab pulsar glitch indicates that the 40-meter radio telescope of the National Time Service Center has a pretty good receiving sensitivity and system stability for pulsar timing observations, and contributes samples to study the mechanism of pulsar glitch.