Tightly regulated downstream load inverters serve as a typical type of constant power load (CPL) in an electrified shipboard power system. It has the risk of dc-link voltage oscillation when cascaded with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$LC$ </tex-math></inline-formula> input filters. This article proposes composite-bisection predictive control (CB-PC) to achieve dc-link voltage stabilization and load voltage control simultaneously. First, an improved general method is proposed to stabilize the dc-link voltage oscillation based on instantaneous power theory, which is valid for finite control set (FCS) model predictive control (MPC) with/without a modulator. Second, deadbeat control is utilized to enhance the transient response of dc-link stabilization. Load voltage control is realized indirectly by tracking an offline-derived inductor-current vector. A droop-akin strategy is devised to strike a trade-off between the two control objectives. Then, a modified bisection algorithm is presented with a tunable iteration number ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> ) to improve the steady-state control performance. It enables the exploitation of surplus computing resources to achieve lower total harmonic distortion (THD) of load voltage. Simulation and experiments validate the effectiveness of the proposed approach, which also illustrates its robustness against parametric variations.