We study how the agency cost implied by the moral hazard problem in a firm dynamics model affects the life cycle growth pattern of firms. In the early stage of a firm's growth, the agency cost restricts the firm's capital input and diminishes over time, so that the firm's growth is driven by efficiency improvements and an exogenous progress in productivity. In the long run, when the firm loses its potential to improve efficiency, growth is driven only by the progress in productivity. As a result of this growth mechanism, consistent with the data, the growth rate and its volatility, as well as Tobin's Q, decrease with age and size. Moreover, the cross-sectional distributions of firm size and managerial compensation obey a power law, as they do in the data. In addition, the model provides novel implications for how the characteristics of the production technology and the preferences of the economic agents affect the growth pattern of firms, and these implications are potentially testable.