A major bottleneck of large-scale water splitting for hydrogen production is the lack of catalysts for the oxygen evolution reaction (OER) with low cost and high efficiency. In this work, we proposed an electrocatalyst of a curved carbon nanocone embedded with two TMN4 active sites (TM = transition metal) and used first-principles calculations to investigate their OER mechanisms and catalytic activities. In the particular spatial confinement of a curved nanocone, we found that the distance between intermediates adsorbed on two active sites is shorter than the distance between these two active sites. This finding can be used to enhance OER activity by distance-dependent interaction between intermediates through two different mechanisms. The first mechanism in which an O2 molecule is generated from two neighboring *O intermediates exhibits a linear activity trend, and the lowest overpotential is 0.27 V for the FeN4 system. In the second mechanism, selective stabilization of the *OOH intermediate is realized, leading to a new scaling relationship (ΔG*OOH = ΔG*OH + 3.04 eV) associated with a modified OER activity volcano (theoretical volcano apex at 0.29 V). The studied mechanisms of the spatial confinement of a carbon nanocone provide a new perspective for designing efficient OER catalysts.