We revisit the F-term hybrid inflation model in supergravity. In particular, we point out that a constant term in the superpotential has significant effects on the inflaton dynamics. It is shown that the hybrid inflation model suffers from several potential problems: tuning of the initial condition, gravitino overproduction and formation of cosmic strings, for both minimal and non-minimal Kähler potentials. These problems can only be avoided in gaugemediated SUSY breaking models where the gravitino is relatively light and the constant term in the superpotential is not important. Implications on the non-thermal leptogenesis scenario are also described.