When the AC voltage is measured precisely based on programmable Josephson voltage standard and differential sampling technology, the amplitude error of sinusoidal signal after multi-period averaging is caused by the unstable phase lock of AC voltage source and incomplete clock synchronization. This paper proposes an error quantitatively evaluation method based on the Monte Carlo method to quantitatively evaluate the amplitude error distribution caused by random jitter of the initial phase within the range of Δφ. The findings reveal that the amplitude error primarily depends on the range of phase jitter and is minimally influenced by the number of averaging cycles. For a jitter range of 5 mrad, the amplitude error can reach a magnitude of 10-6. To address this, a compensation method based on the phase jitter range is proposed. By calculating the compensation coefficient and applying the correction, the amplitude error caused by phase jitter is significantly reduced. The compensation effect improves with an increasing number of averaging cycles when the jitter range is fixed. A verification experiment was conducted to validate the proposed compensation method. For a jitter range of 50 mrad, the amplitude error exceeded 1×10-4 V/V after multi-period averaging but was reduced to a magnitude of 10-6 magnitude. These results confirm the effectiveness of the proposed method.