This paper takes a kind of 3-UPS Parallel Machine Tool (PMT) as the objective of research. First, the kinematic analysis is carried out to the machine and the kinematics equation is obtained. Then, the mathematical model on tool posture error of this machine is established in considering the joint gap based on the kinematics equation. According to the mathematical model expression, the posture error of tool tip point can be calculated when the specific values to the length error of the driving rod and the position error of the joint point are known. The establishment of error model has important theoretical significance to the design as well as the error analysis and compensation of this Parallel Machine Tool.