This paper presents a method of constructing anticipatory monitors for P_ALTL (parameterized LTL (linear temporal logic)) based on automata theory. This paper on one hand investigates into the important concepts about the syntax, anticipatory semantics, valuation generation and binding of P_ALTL. It is assured that the binding and using are correct in syntax level. Then the concept of parameterized anticipatory monitor is presented consisting of the static part and the dynamic part. The static part is presented as parameterized Büchi automata, and the dynamic part is composed of the valuations of variables in the current state. While the system running, based on the static parameterized Büchi automata, the valuations of variables are dynamically generated and bound from the current state in an on-the-fly fashion, and the anticipatory monitor incrementally checks whether the current running system is satisfied with the given parameterized property. In this process, the parameterized monitor can precisely identify the minimal good/bad prefix of the monitored property.