The singularity of a 6-PRRS parallel robot is studied based on Jacobins matrix. For forward singularity

the Jacobins matrix is obtained based on velocity projection

a new notion of spatial instantaneous axis is introduced

and the expressive form of the parallel mechanism singularity is given when it is generated. For inverse singularity

the parallel robot is divided into several series mechanisms

and the Jacobins matrix of these series mechanisms is solved by the exponential product equation and proved to be singular when the series mechanisms are singular. Based on forward or inverse singularity

a more special composite singular phenomena is proposed

which is generated when the forward and inverse singularities occur simultaneously under a certain spatial pose

and its possible existent form is given. The solving process of Jacobins matrix

the proving of matrix singularity and the description of the mechanism singularity provide a new and intuitional method for studying the singularity of parallel mechanism.