Transient analysis is an indispensable tool for analyzing the voltage fluctuation of distribution systems according to the penetration of distributed generations with grid-connected inverters. Electromagnetic transient (EMT) analysis is suitable for the purpose because it enables detailed modeling of the inverters and accurate simulation of their dynamic behavior. However, the EMT analysis requires a smaller calculation time step by a factor of 500 if the simulated power system includes the inverters. Simulation of the inverters is a bottleneck in speeding up the EMT analysis. This paper proposes a novel average-value modeling method for the grid-connected inverters. The proposed inverter model operates in a larger calculation time step, and speeds up the EMT analysis of distribution systems containing the inverters. The maximum error in the output power was 8% compared to the result by the conventional model. Dynamic voltage simulations are demonstrated with a test case, which includes tap changing transformers with a voltage controller and a photovoltaic generation facility. The proposed model reduces the required calculation time by a factor of 754 compared to the conventional model whereas there is no significant difference in the simulated result.