A novel n(4-SPS+SP) serial-parallel manipulator (S-PM) formed by n 4-SPS+SP PMs with four degrees of freedom (DOF) connected in series is proposed in this paper. The kinematics, statics and stiffness model of this serial-PM is established. First, the forward kinematics of 4-SPS+SP (spherical joint-prismatic joint-revolute+spherical joint-prismatic joint) PM is derived and the kinematics of n(4-SPS+SP) S-PM is studied combined with the kinematics result of single 4-SPS+SP PM. Second, the statics, deformation and stiffness of n(4-SPS+SP) S-PM are studied. Finally, an analytically solved example is given for 3(4-SPS+SP) formed by three 4-SPS+SP PMs. The method for this mechanism is fit for other S-PMs.