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Based on force screw equilibrium equation of a kind of 6_PUS parallel mechanism and decomposed force of its branches, force Jaccobian was derived and then kinematic Jaccobian was got. By kinematic Jaccobian, singurality conditions of 6_PUS parallel mechanism were achieved and the geometry characteristics in two kinds singularities of this parallel mechanism were drawn. In order to study conveniently on singularities of the mechanism in its’ full work space, a concept that called singularity field was put forward to express the mechanism actually running. As the base to research singularity and to avoid singularity, the expression equations of singularity field were built. The distribution of two kinds of singularities in full work space of this 6_PUS mechanism was obtained and methods for avoid singularities or forbid mechanism running at singularities point were brought out for reference to design of this kind mechanism. 