Under the ambitious goal of carbon neutralization, photovoltaic (PV)-driven electrolytic hydrogen (PVEH) production is emerging as a promising approach to reduce carbon emission. Considering the intermittence and variability of PV power generation, the deployment of battery energy storage can smoothen the power output. However, the investment cost of battery energy storage is pertinent to non-negligible expenses. Thus, the installation of energy-storage equipment in a PVEH system is a complex trade-off problem. The primary goals of this study are to compare the engineering economics of PVEH systems with and without energy storage, and to explore time nodes when the cost of the former scenario can compete with the latter by factoring the technology learning curve. The levelized cost of hydrogen (LCOH) is a widely used economic indicator. Represented by seven areas in seven regions of China, results show that the LCOH with and without energy storage is approximately 22.23 and 20.59 yuan/kg in 2020, respectively. In addition, as technology costs drop, the LCOH of a PVEH system with energy storage will be less than that without energy storage in 2030.