The linearized Euler equations (LEEs) solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN) configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.