The growth of stable and efficient catalysts is vital for the electrochemical hydrogen evolution reaction (HER). Metal–organic frameworks (MOFs) have been recognized as ideal templates for fabricating efficient nanomaterial-based electrocatalysts for the HER. In this study, nitrogen-containing Co-MOF (ZIF-67), Co-MOF-74, and cobalt chloride salt were selenized to create various cobalt-selenide-based materials, i.e., cobalt selenide@nitrogen-doped carbon (CoSe2@NC), CoSe2@C, and CoSe2, respectively. The core–shell structure of CoSe2@NC originated from ZIF-67 exhibited better HER catalytic activity than those of CoSe2@C and CoSe2. CoSe2@NC exhibited a low overvoltage of 184 mV at 10 mA cm−2 and a small Tafel slope of 58.4 mV dec−1. In addition, this catalyst exhibited excellent durability while maintaining its performance after 12 h of testing. The high catalytic activity is ascribed to the integrated effect of the core–shell architecture, N-doped carbon, and large surface area, making protected active sites, high conductivity, and exposed active sites possible. The results demonstrate the efficiency of using MOFs as precursors for cobalt selenide fabrication and provide a potential synthetic strategy for noble-metal-free electrocatalysts for hydrogen production.