An algorithm for model checking value-passing processes is presented. Processes are modeled as symbolic transition graphs with assignments. To specify properties for such processes a graphical predicate mu-calculus is introduced. It allows arbitrary nesting of the least and greatest fix-points, and contains the propositional mu-calculus as a proper subset. The algorithm instantiates input variables on-the-fly and states are only generated when they are needed for the computation. To handle alternating fix-points properly, a multi-stack is employed an the controlling strategy is such that a state is evaluated without depending on the default values for more deeply nested states. The algorithm is shown correct with respect to the semantics of the predicate mucalculus. Its complexity is also analysed.