The theory of a sampling method for measuring the average parameters of AC voltage, current and power is analyzed, and a condition without introducing measurement error is given. The reasons for measurement error of AC parameters caused by non-synchronous sampling and the mechanism of window function weighted method to suppress measurement error are analyzed. Rectangular convolution windows, which are most effective in suppressing errors in the case of very small non-synchronous frequency deviation, and measurement error formulae are presented. Considering the DC component in the input signal of ADC circuit in practice, a series of formulae corresponding to the convolution window weighted algorithm for AC parameter measurement are derived. These are suitable for direct implementation by an MCU. The number of machine cycles and the length of time for the MCU to execute the convolution window weighted algorithm are tested by simulation. The results show that the convolution window weighted algorithm is time efficient. The calculation of one sampling point in the AC parameter measurement of 2-order convolution window weighted algorithm can be completed using a STM32 MCU in only a small part of the sampling period. This work is supported by National Natural Science Foundation of China (No. 6164006).