The creation of effective autonomous agents (bots) for combat scenarios has long been a goal of the gaming industry. However, a secondary consideration is whether the autonomous bots behave like human players; this is especially important for simulation/training applications which aim to instruct participants in real-world tasks. Bots often compensate for a lack of combat acumen with advantages such as accurate targeting, predefined navigational networks, and perfect world knowledge, which makes them challenging but often predictable opponents. In this paper, we examine the problem of teaching a bot to play like a human in first-person shooter game combat scenarios. Our bot learns attack, exploration and targeting policies from data collected from expert human player demonstrations in Unreal Tournament. We hypothesize that one key difference between human players and autonomous bots lies in the relative valuation of game states. To capture the internal model used by expert human players to evaluate the benefits of different actions, we use inverse reinforcement learning to learn rewards for different game states. We report the results of a human subjects' study evaluating the performance of bot policies learned from human demonstration against a set of standard bot policies. Our study reveals that human players found our bots to be significantly more human-like than the standard bots during play. Our technique represents a promising stepping-stone toward addressing challenges such as the Bot Turing Test (the CIG Bot 2K Competition).