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This paper considers a bi-criteria scheduling on parallel machines in fuzzy environment which optimizes the weighted flow time and maximum tardiness. The fuzziness, vagueness or uncertainty in processing time of jobs is represented by triangular fuzzy membership function. The bi-criteria problem with weighted flow time and maximum tardiness as primary and secondary criteria, respectively, for any number of parallel machines is NP-hard. So, a heuristic algorithm is proposed to find the optimal sequence of jobs processing on parallel machines so as to minimize the secondary criterion of maximum tardiness without violating the primary criterion of weighted flow time. A numerical illustration is also given in support of the algorithm proposed.