The limiting factor for quantitative analysis of Markov decision processes (MDP) against specifications given in linear temporal logic (LTL) is the size of the generated product. As recently shown, a special subclass of limit-deterministic Büchi automata (LDBA) can replace deterministic Rabin automata in quantitative probabilistic model checking algorithms. We present an extension of PRISM for LTL model checking of MDP using LDBA. While existing algorithms can be used only with minimal changes, the new approach takes advantage of the special structure and the smaller size of the obtained LDBA to speed up the model checking. We demonstrate the speed up experimentally by a comparison with other approaches.