This paper develops a concurrent and parallel garbage collection (GC) method that works with a lightweight thread library realizing the standard ``user–worker'' thread model. The GC algorithm is organized as a set of procedures that are called from a user thread at various occasions and executed in the context of the worker threads owning the user thread. The procedures realize an on-the-fly collection that does not stop any thread. All worker threads cooperatively perform the collection in parallel. This construction achieves the same degree of parallelism as underlying lightweight thread scheduling. We have implemented the algorithm in a Standard ML compiler and have evaluated the performance with sequential and parallel benchmark programs. Our implementation shows good parallel scalability comparable to C programs directly using the lightweight threads library.