The battery-electric mining haul truck (MHT) enables zero tailpipe emissions and reduces operating costs if coupled with sufficient renewable energy generation. However, the quick degradation of the onboard battery energy storage system increases lifecycle operating costs. This study introduced the hybrid energy storage system (HESS) to slow down battery degradation. The design problem was formulated to minimize the life cycle cost, including the electricity consumption and the component's degradation costs. The sizing of lithium batteries and ultracapacitors was optimized, subject to the physical limitations. On the other hand, the power distribution between battery and ultracapacitors also impacts the lifecycle costs. In the design optimization problem, the power allocation between batteries and ultracapacitors was optimized by dynamic programming. The nested optimization results indicate that the lifecycle cost of HESS can be reduced by as much as 23.94 percent. The overall weight and volume of HESS is slightly less than the battery energy storage system, decreased by 1.06 percent and 2.56 percent, ensuring achievable layouts. This study introduces a feasible solution and methods to optimize the HESS mining haul truck.