Summary: We study computation of a controllable sublanguage of a given non-prefix-closed regular specification language for an unbounded Petri net. We approximate the generated language of the unbounded Petri net by a regular language, and compute the supremal controllable sublanguage of the specification language with respect to the regular language approximation. This computed language is a controllable sublanguage with respect to the original generated language of the unbounded Petri net, but is not necessarily the supremal one. We then present a sufficient condition under which the computed sublanguage is the supremal controllable sublanguage with respect to the original generated language of the unbounded Petri net.