Energy management strategy (EMS) plays a crucial role in improving the fuel economy of fuel cell hybrid electric vehicles (FCHEV). In this paper, an alternating direction method of multipliers-based distributed interior point based EMS is proposed for FCHEV equipped with fuel cell (FC), battery (BAT), and ultracapacitor to reduce hydrogen consumption, improve fuel economy and extend the service life of energy sources. To mitigate the impact of peak power on FC and BAT, an adaptive fuzzy filter is employed to decouple the power demand frequencies. Subsequently, the adaptive equivalent consumption minimization strategy (A-ECMS) is proposed to enhance fuel economy. Since A-ECMS is a common local optimization problem characterized by non-convexity, an enhanced convex optimization theory is proposed to convert the non-convex problem into a convex one. The convex problem is then solved using an alternating direction method of multipliers-based distributed interior point method based EMS for FCHEV to enhance computational efficiency and convergence performance. Simulation results conclusively illustrate that the proposed EMS enhances the fuel economy of FCHEV, reduces power fluctuations of FC, and improves computational efficiency when compared to Convex optimization and the interior point method.