This article considers an investor who has an exogenous cash flow evolving according to a Levy process and invests in a financial market consisting of only risky assets, whose prices are governed by exponential Levy processes. Two continuous-time portfolio selection problems are studied for the investor. One is a benchmark problem, and the other is a mean-variance problem. The first problem is solved by adopting the stochastic dynamic programming approach, and the obtained results are extended to the second problem by employing the duality theory. Closed-form solutions of these two problems are derived. Some existing results are found to be special cases of our results.