In this paper, we present a numerical investigation of various types of drops detaching from an axisymmetric, laminar compound jet of immiscible fluids. The compound jet flows in a co-flowing immiscible outer fluid. We use a front-tracking/finite difference method to track the unsteady evolution and breakup of the compound jet which is governed by the Navier-Stokes equations for incompressible and Newtonian fluids. Numerical results show that depending on flow parameters, the compound jet can break up into different types of drops: simple drops, single-core compound drops and multi-core compound drops.