Solar sail is one of the promising propulsion systems for future deep space exploration missions as it does not require any fuel to acquire propulsive force. However, the attitude control system of the solar sail, which controls the direction of the sail and thus the propulsive force, has not been much studied, although this constitutes the essential part of the orbital control using solar sail. This paper discusses the attitude dynamics and the control method of a spinning type solar sail spacecraft. The spinning type solar sail has no rigid structure supporting its membrane. This type of mechanism has the advantage in its simple and lightweight structure, however, the attitude control is difficult due to the flexibility of the membrane. In this paper, we introduced a mathematical dynamics model including first vibration mode of the membrane which can handle coupled motion of a rigid spacecraft and a flexible membrane, and analytically developed a controller that can avoid unnecessary oscillatory motion. The performance of the controller and the effect of solar radiation pressure, which can deform the membrane of solar sail, on the controller were verified by numerical simulations using more precise multi-particle numerical model.