A new simulation method for solving fluid-structure two-way coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A new definition of velocity-vorticity formulation aids us to introduce an immersed boundary method that does not require a force term to impose the no-slip condition on the solid boundaries. The proposed method is easy to implement and apply for two-way fluid-structure interaction problems. The dynamics of a falling and rising circular cylinder in a quiescent fluid as well as the motion of a circular cylinder in a lid-driven cavity are considered to evaluate the capabilities of the presented method.