The flow of a viscous incompressible fluid past an accelerated vertical circular cylinder in a rotating fluid is analyzed in this study. The cylinder starts impulsively from rest with uniform acceleration in its own plane relative to the rotating fluid. The closed form solutions of the governing boundary layer equations in non-dimensional form are obtained in terms of Bessel functions and modified Bessel functions by Laplace transform technique. Numerical values of the axial velocity, transverse velocity and temperature profiles are obtained for various physical parameters and presented in graphs. Skin friction and Nusselt number are also discussed graphically.