It is well known that the forward kinematics of parallel robots is a very difficult problem. Closed-form forward kinematics solutions have been reported only to a few special classes of parallel robots. This paper presents closed-form forward kinematics solutions of a 4-DOF parallel robot H4. A 16th order polynomial in a single variable is derived to solve the forward kinematics of the H4. The 16 roots of the polynomial lead to at most 16 different forward kinematics solutions. A numerical verification is also presented.