Vehicle delay is an important measure to evaluate the signal timings of signalized intersections. When optimization the signal control parameters, delays of vehicles from all approach directions of an intersection should be considered. Based on the analysis of the vehicle delay on an approach of intersection, directed against the typical condition of a congested intersection—over-saturated condition, the paper has analyzed and inferred the intersection delay dynamic formulation, and has established the relation between intersection delay, the signal timings, vehicle arrival rate and the queue lengths, and that provides useful information for understanding vehicle delay of signalized intersection and for establishing performance index function of signal timing optimization. Vehicle delay is an important measure to evaluate the signal timings of signalized intersections. When optimization the signal control parameters, delays of vehicles from all approach directions of an intersection should be considered. Based on the analysis of the vehicle delay on an approach of intersection, directed against the typical condition of a congested intersection-over-saturated condition, the paper has been analyzed and inferred the intersection delay dynamic formulation, and has established the relation between intersection delay, the signal timings, vehicle arrival rate and the queue lengths, and that provides useful information for understanding vehicle delay of signalized intersection and for establishing performance index function of signal timing optimization.