We study a generalization of the recently introduced order-preserving pattern matching, where instead of looking for an exact copy of the pattern, we only require that the relative order between the elements is the same. In our variant, we additionally allow up to k mismatches between the pattern and the text, and the goal is to construct an efficient algorithm for small values of k. For a pattern of length m and a text of length n, our algorithm detects an order-preserving occurrence with up to k mismatches in O(n(loglogm + kloglogk)) time.