This paper presents an INS (inertial navigation system) for an AGV (automatic guided vehicle) with Mecanum wheels. An omni wheel or a Mecanum wheel, which has rollers attached to a conventional wheel, facilitates omni-directional driving. Most positioning systems use the encoder because it can measure precisely the rotation of the wheel. However, it is difficult to accurately calculate the position of an AGV with omni wheels or Mecanum wheels because slips occur frequently in the rollers attached to the wheels. Therefore, many studies have been carried out to compensate for the weakness of the encoders by fusing an accelerometer and a gyro sensor. However, there is still a rapid increase in the number of errors, owing to the second integral of an accelerometer. Hence, this paper proposes an INS for an AGV with Mecanum wheels. The proposed system integrates an encoder, an accelerometer, and a gyro sensor through two Kalman filters. To verify the performance of the proposed INS, we analyzed the positioning accuracy of an AGV by studying straight, sideways, and diagonal movements over a 250 cm distance in a 300 cm ${ imes}$ 300 cm space at speeds of about 200 and 380 mm/s. The results of the experiment showed that the proposed INS can measure effectively the position of an AGV, despite frequent slips.