A rotating electric machine, which can achieve improvement of a reluctance torque, reduction of stress and improvement of a power factor at the same time, and can also realize high output, and an electrically driven vehicle having the rotating electric machine are provided. A permanent magnet is arranged on a q-axis that connects magnetic poles of a rotor; a gap is formed in a radial direction of the permanent magnet; another permanent magnet is arranged facing the said permanent magnet so that these permanent magnets may sandwich a d-axis which connects centers of the magnetic poles; and another gap is formed at a position corresponding to a position of the said gap. Further, a first virtual line that coincides with a boundary of a permanent magnet insertion hole, which is arranged facing the d-axis, on an inner circumference side of a rotor core; and a second virtual line that is concentric with an inner circumference of the rotor core and contacts the first vertical line are set so that the second virtual line on the innermost circumference and the first virtual line have two or more tangent points.