Control delay is the primary measure for determination of the level of service of signalized intersections. The existing analytical delay models usually work well for isolated intersections, but are not as effective when applied to diamond interchanges. The limited storage space between the two closely spaced intersections of a diamond interchange may cause queue spillback from the internal link to the outside roads. This property would give rise to unrealistic delay calculations for diamond interchanges with high traffic volumes. This paper describes the development of a new analytical delay model that takes into account the effects of internal queue spillback at diamond interchanges. Simulation studies are conducted to compare the effectiveness of the proposed approach with existing methods. The study shows that for low-overlap time conditions, the proposed model tends to agree with the Synchro and VisSim simulations and is better than Elefteriadou's method, which tends to overpredict delay. For high overlaps, the Elefteriadou method, VisSim simulation, and the proposed model tend to agree, while Synchro diverges significantly by overestimating delay. The study contributes to the literature and practice by providing an open-source analytical model that can either be used as a stand-alone delay calculation model or as a supplement to the existing methods.