Skill management is a key factor in improving effectiveness of industrial companies, notably their maintenance services. The problem considered in this paper concerns scheduling of maintenance tasks under resource (maintenance teams) constraints. This problem is generally known as unrelated parallel machine scheduling. We consider the problem with a both objectives of minimizing total weighted tardiness (TWT) and number of tardiness tasks. Our interest is focused particularly on solving this problem under skill constraints, which each resource has a skill level. So, we propose a new efficient heuristic to obtain an approximate solution for this NP-hard problem and demonstrate his effectiveness through computational experiments. This heuristic is designed for implementation in a static maintenance scheduling problem (with unequal release dates, processing times and resource skills), while minimizing objective functions aforementioned.