The Model Predictive Control (MPC) scheme of AC/DC matrix converters (MCs) conventionally requires voltage information at two sides of the input filter to predict the control variables. The voltage sensor is usually used to measure these voltage values, which increases the hardware volume and cost and may reduce the control reliability due to the risk of sensor malfunction. To overcome this problem, this paper presents a voltage sensorless MPC scheme with cascade voltage estimation algorithm to estimate the voltage information at both two sides of the input filter. The AC input voltage is estimated firstly by considering its relationship between the switching state and the grid current. Then, the grid voltage is estimated by applying the virtual flux concept, which is originally presented to control the voltage source converters. Simulation results are given to verify the effectiveness of the proposed voltage sensorless MPC scheme.