The theory of jet instabilities has been developed under several assumptions, which include the assumption that the jets are steady. The common-rail diesel fuel injection systems utilizing pulsed injection have drastically improved the ability to lower emissions, noise, and fuel consumption. However, with the application of the injection techniques in modern engines, the unsteady effects introduced by the pulsed injection are yet to be fully investigated. These unsteady effects may be attributed to some of the deviations observed in the literature between theoretical predictions and experimental data. The present paper has been able to demonstrate through analytical means that unsteady effects of liquid jet have significant impacts on the instability and breakup of liquid fuel. The model was developed from the Navier-Stokes equation with linear perturbations, which considers transient base flow parameters. Results obtained have good agreement with experimentally obtained data for penetration length and spray angle.