This paper took a 3-TPT Parallel Robot as the object to study its singularity within the workspace. Firstly the kinematics equation of Parallel Robot was established according to the kinematics analysis and the Jacobian matrix of parallel mechanism could be obtained at the same time. Then the workspace of Parallel Robot was carried on the solution and the analysis. Finally the degree of operability was taken as the measure index to analyze the singularity of Parallel Robot within the workspace, and the results showed that this Parallel Robot does not have singular position. The analysis results of this paper have laid the theoretical foundation for the position control and processing track planning of this Parallel Robot.