A fully digital beam position and phase measurement (BPPM) system was designed for the linear accelerator (LINAC) in Accelerator Driven Sub-critical System (ADS) in China. Phase information is obtained from the summed signals from four pick-ups of the Beam Position Monitor (BPM). Considering that the delay variations of different analog circuit channels would introduce phase measurement errors, we propose a new method to tune the digital waveforms of four channels before summation and achieve real-time error correction. The process is based on the vector rotation method and implemented within one single Field Programmable Gate Array (FPGA) device. Tests were conducted to evaluate this correction method and the results indicate that a phase correction precision better than +/- 0.3 degree over the dynamic range from -60 dBm to 0 dBm is achieved.