We developed a coupled finite difference level set projection code for the simulation of viscoelastic ink droplet ejections. The ink is modeled by the Oldroyd-B viscoelastic fluid model, which is decent for dilute polymer solutions, while the air is modeled as a Newtonian fluid. A slipping contact line model was implemented to resolve the contradiction of the moving contact line and the noslip condition. For practical applications, the code was connected to an equivalent circuit, which simulates the interior ink flow considering the influence of ink cartridge, vibration plate, and PZT actuator. Simulation examples showing the effect of fluid elasticity will be presented.