An apparatus for tripping oil pipe and a system for automatic well workover comprises an elevator transfer device for transferring an elevator connected with an oil pipe, the elevator transfer device being structured for enabling continuous, automatic tripping operations of the oil pipe. The elevator transfer device comprises a lifting assembly used for lifting and releasing an oil pipe engaged with the elevator, and an elevator transport assembly used for transferring an elevator at a wellhead and/or an elevator on the lifting assembly. The apparatus for tripping oil pipe can lower the labor intensity and improve operation safety.