The invention relates to a non-circular gear transmission case and a transmission mechanism thereof. The transmission mechanism is a combined type transmission mechanism with a non-uniform velocity ratio, comprising a non-circular gear transmission case (24), a low speed motor (20), a chain wheel train (21, 22, 23) or a belt wheel train. The output torque and the output rotating speed of the transmission mechanism are consistent with a mainframe load change form; therefore, the transmission mechanism can save energy by a big margin when being used in a mechanism requiring transmission with a non-uniform velocity ratio. The pitch curve shape of non-circular gears (27, 28), and geometric and initial position parameters are determined by an optimized design according to the mainframe load change form, continuity of the pitch curve and fabrication procedure and the like. When the non-circular gears (27, 28) are connected with a circular gear train and a circular gear planetary gear train power, non-circular gear transmission cases of various forms can be formed. An energy-saving beam pumping unit can be formed by removing a speed reducer, a belt wheel and an electric motor and installing the non-circular gear transmission case and the transmission mechanism thereof on a conventional beam pumping unit.