This paper, deals with application of the Secant-Bootstrap Method (SBM) to solve the Closed-form forward kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. This methodology has been utilized to achieve approximate solutions for nonlinear equations of kinematic of Tip-Tilt-Piston (T.T.P) Parallel Manipulator. The SBM is a novel methodology which moderate disadvantage of the traditional numerical techniques. The excellent agreement of the Secant-Homotopy Continuation solutions with the traditional numerical methods such as the Newton–Raphson method could be established without aberration. SBM for the forward kinematic of T.T.P Parallel Manipulator leads to 16 solutions that are eight pairs of reflected configurations with respect to the base plane.