Team orienteering, an extension of single-competitor orienteering, is the problem of determining multiple paths from a starting node to a finishing node for a given allowed time or distance limit fixed for each of the paths with the objective of maximizing the total collected score. Each path is through a subset of nodes, each of which has an associated score. The team orienteering problem has many applications such as home fuel delivery, college football players recruiting, service technicians scheduling, military operations, etc. Unlike existing optimal and heuristic algorithms often leading to heavy computation, this paper suggests two types of priority rule based heuristics-serial and parallel ones-that are especially suitable for practically large-sized problems. In the proposed heuristics, all nodes are listed in an order using a priority rule and then the paths are constructed according to this order. To show the performances of the heuristics, computational experiments were done on the small-to-medium sized benchmark instances and randomly generated large sized test instances, and the results show that some of the heuristics give reasonable quality solutions within very short computation time.