This paper considers the problem of scheduling n jobs on m parallel unbounded batch machines to minimize the total weighted completion time. Each job is characterized by a positive weight, a release time and a processing time. Each unbounded batch machine can process up to B (B≥n) jobs as a batch simultaneously. The processing time of a batch is the longest processing time among jobs in the batch. Jobs processed in the same batch have the same completion time, i.e., their common starting time plus the processing time of the batch. A polynomial time approximation scheme (PTAS) for this problem is presented.