This paper proposes an enhanced measure of accessibility that explicitly considers circumstances in which the capacity of the transport infrastructure is limited. Under these circumstances, passengers may suffer longer waiting times, resulting in the delay or cancellation of trips. Without considering capacity constraints, the standard measure overestimates the accessibility contribution of transport infrastructure. We estimate the expected waiting time and the probability of forgoing trips based on the M/GB/1 type of queuing and discrete-event simulation, and formally incorporate the impacts of capacity constraints into a new measure: Capacity Constrained Accessibility (CCA). To illustrate the differences between CCA and standard measures of accessibility, this paper estimates the accessibility change in the Beijing–Tianjin corridor due to the Beijing–Tianjin Intercity High-Speed Railway (BTIHSR). We simulate and compare the CCA and standard measures in five queuing scenarios with varying demand patterns and service headway assumptions. The results show that 1) under low system loads condition, CCA is compatible with and absorbs the standard measure as a special case; 2) when demand increases and approaches capacity, CCA declines significantly; in two quasi-real scenarios, the standard measure overestimates the accessibility improvement by 14~30% relative to the CCA; and 3) under the scenario with very high demand and an unreliable timetable, the CCA is almost reduced to the pre-BTIHSR level. Because the new CCA measure effectively incorporates the impact of capacity constraints, it is responsive to different arrival rules, service distributions, and system loads, and therefore provides a more realistic representation of accessibility change than the standard measure.