We report the detection of a glitch event in the Vela pulsar, which occurred on 12 December 2016, based on the timing data obtained from observations between January 2016 and February 2018 at frequency centered at 2256 MHz using the Kunming 40-m radio telescope. The timing solutions for the pre- and post-glitch are presented. By fitting the glitch model to the timing data, we found that the post-glitch recovery exhibits two terms with exponential decay with the time scales of 1 d and 6 d, respectively. The glitch parameters are determined with g/=1.431(2)x10-6 and g/=73.354x10-3. The value of the coupling parameter is calculated to be approximate to 0.08, implying that the core superfluid is probably not involved in this event. For the glitches with two or more terms with exponential decay in the Vela pulsar, we show that the exponential decays usually exhibit longer time scales with higher degree of glitch recovery. The post-glitch behavior in the slow-down rate is dominated by a linear decrease process. From detection of the variations in the slopes of the spin-down rates after the exponential recoveries of the 2013 and 2016 glitches, we conclude that no persistent shift was involved in the 2016 glitches.