In this paper we present a concept of a multirotor unmanned aerial vehicle (UAV) capable of horizontally moving without tilting the vehicle body. The concept is based on the moving mass control, which we have recently proposed for roll and pitch control of a large multirotor UAV with internal combustion engines (ICEs). The vehicle is comprised of four ICEs with rotors tilted towards the body center and four moving masses, each placed in a motor arm. We give a complete 6 degrees of freedom (DOF) mathematical model in the form of nonlinear differential equations, which we linearize to obtain transfer functions. The models are used to design a control system comprised of state space controllers for roll/pitch stabilization and PID controllers for height, yaw and velocity control. The concept is verified in the Gazebo simulator and experimentally on a 2DOF laboratory gimbal.