The Tianlai Dish Pathfinder Array is a radio interferometer array consisting of 16 six-meter dish antennas. The original digital backend integration time is at the seconds level, designed for H i intensity mapping experiment. A new digital backend with millisecond response is added to enable it to search for fast radio burst during its observations. The design and calibration of this backend, and the real time search pipeline for it are described in this paper. It is capable of forming 16 digital beams for each linear polarization, covering an area of 19.6 square degrees. The search pipeline is capable of searching for, recording and classifying FRBs automatically in real time. In commissioning, we succeeded in capturing the signal pulses from the pulsars PSR B0329+54 and B2021+51.