In RFID systems, one important issue is how to effectively address tag collision, which occurs when multiple tags reply simultaneously to a reader, so that all the tags are correctly identified. However, most existing anti-collision protocols assume isotropic collisions where a reader cannot detect any of the tags from the collided signals. In practice, this assumption turns out to be too pessimistic since the capture effect may take place, in which the reader considers the strongest signal as a successful transmission and the others as interference. In this case, the reader disregards the other collided tags, and in turn, fails to read the tag(s) with weaker signal(s). In this paper, we propose a capture effect-aware anti-collision protocol, called Multi-Round Collision Tree (MRCT) protocol, which efficiently identifies the tags in real RFID environments. MRCT deals with the capture effect as well as channel error by employing a multi-round based identification algorithm. We also analyze the performance of MRCT in terms of the number of slots required for identifying all tags. The simulation results show that MRCT significantly outperforms the existing protocol especially in a practical environment where the capture effect occurs.