Generating core-shell particles with a well-controlled morphology is of great interest due to the interdependence between the morphology and different properties of these structures. These particles are often generated in microfluidic devices in a background quadratic flow. Therefore, in this study, we investigate the hydrodynamics and morphology of a concentric active compound particle, an active particle encapsulated in a fluid droplet, in an imposed quadratic flow. Governing equations for fluid flow are analytically solved in the inertia-less limit assuming that the surface tension force dominates the viscous forces (capillary number, Ca ≪ 1). Poiseuille flow deforms the compound particle into a three-lobe structure governed by the hexapolar component of the Poiseuille flow. Activity deforms the compound particle into a prolate shape owing to the velocity field of a force dipole. For an active compound particle in a Poiseuille flow, morphology is sensitive to the orientations and relative strengths of the activity and Poiseuille flow. Primarily, the presence of activity breaks the three-lobe symmetry of the drop shape and makes it more asymmetric and elongated. Moreover, the active compound particle becomes more susceptible to breakup in a quadratic flow when (i) the strength of activity is much stronger than the imposed flow strength, (ii) the active particle is oriented along the symmetry axes of the quadratic flow, (iii) the size ratio of the confining droplet to the encapsulated active particle is small and (iv) the viscosity ratio of the outer fluid to the inner fluid is small. Finally, we demonstrate that imposing the pulsatile quadratic flow prevents the breakup of an active compound particle during its generation and transport, and further assists in tuning the morphology.