We study the model-checking problem for a quantitative extension of the modal mu-calculus on a class of hybrid systems. Qualitative model checking has been proved decidable and implemented for several classes of systems, but this is not the case for quantitative questions that arise naturally in this context. Recently, quantitative formalisms that subsume classical temporal logics and allow the measurement of interesting quantitative phenomena were introduced. We show how a powerful quantitative logic, the quantitative mu-calculus, can be model checked with arbitrary precision on initialised linear hybrid systems. To this end, we develop new techniques for the discretisation of continuous state spaces based on a special class of strategies in model-checking games and present a reduction to a class of counter parity games.