Radial velocity (RV) variable stars are important in astrophysics. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) spectroscopic survey has provided ~6.5 million stellar spectra in its Data Release 4 (DR4). During the survey ~4.7 million unique sources were targeted and ~1 million stars observed repeatedly. The probabilities of stars being RV variables are estimated by comparing the observed RV variations with simulated ones. We build a catalog of 80702 RV variable candidates with probability greater than 0.60 by analyzing the multi-epoch sources covered by LAMOST DR4. Simulations and cross-identifications show that the purity of the catalog is higher than 80%. The catalog consists of 77% binary systems and 7% pulsating stars as well as 16% pollution by single stars. 3138 RV variables are classified through cross-identifications with published results in literatures. By using the 3138 sources common in both LAMOST and a collection of published RV variable catalogs, we are able to analyze LAMOST's RV variable detection rate. The efficiency of the method adopted in this work relies not only on the sampling frequency of observations but also periods and amplitudes of RV variables. With the progress of LAMOST, Gaia, and other surveys, more and more RV variables will be confirmed and classified.