A mobile emissions control system having an emission capturing system and emission control system is provided for diesel engines operated on ocean-going ships at-berth. The emissions control system may be mounted on a towable chassis or mounted on a barge, allowing it to be placed alongside ocean-going ships at-berth. A crane or boom transfers a duct of the emissions capturing system extending from the emissions control system to the ship to capture exhaust from its engine. Alternatively, the system may be mounted on an automated guided vehicle (AGV) equipped with a tower and a crane. The crane mounted on the AGV then lifts the duct forming part of the emissions capture system to the ship's exhaust system to capture exhaust from the ship's diesel engine and transfers it to the emissions control system, which cleans the exhaust and then passes clean air into the atmosphere through an exhaust outlet.