This paper reformulates and generalizes the classical Uzawa-Lucas model of economic growth and human capital accumulation by representing time as a discrete variable and using a population law with non-constant growth rate. In addition, the model is developed by using a more general utility function than the original. In this setup, the model can be represented by a four-dimensional dynamical system, which admits a unique optimal trajectory in human and physical capital and consumption. It is shown that there is a unique non-trivial equilibrium. The results of the study are compared with the original model in discrete time.