The temple, located at 7 Leon Pozemsky Street, is situated in the Zapskovye area, across the Pskova River. This street was previously called Zvanitsa and later, Narvskaya. The name "with Primostye" indicates that the church is located by the bridge. The monument complex includes the church itself, the foundation of the ancient bell tower, and a fence with gates.

The exact date of the construction of the Church of Cosmas and Damian with Primostye is unknown, but the first mention of it in the Pskov chronicles dates back to 1458, when the wooden church burned down in a fire. By that time, the temple was already the center of the Kozmodemyansk district. A new stone church was laid nearby and completed in 1463.

The church was the main one in the area, where the Konchanskaya veche took place. The construction involved not only local residents but also the prince and the posadnik, highlighting its importance for all of Pskov.

The church has burned multiple times, but the most destructive fire occurred in 1507 due to a gunpowder explosion. The restoration after this fire led to the reconstruction of the temple. Yu.P. Spegalsky notes that after 1507, the church received an eight-pitched roof and a new dome. A large four-bay bell tower was also built with the church on top and storages below, protected from fire. This building stood at the corner of the intersection, dividing the flow of people into two streets.

In the 17th century and later, the church's chapels underwent reconstructions, and nothing remains from the 15th and 16th centuries. In the 18th century, the pillars of the bell tower were demolished, and an octagonal bell tower was built in their place, which stood until the Great Patriotic War.

The gates of the Kozmodemyansk church are a rare example of such structures. They have not survived in their original form. Above the archway, a depression is visible where a fresco depicting Cosmas and Damian once was. The upper part of the niche was destroyed along with the pediment that completed the gates. The church's porch, added to the narthex, dates back to the 17th century and shows signs of numerous alterations.

During the Great Patriotic War, the temple suffered greatly. The materials of the commission investigating the crimes of the German-fascist invaders mention that the roofs and wooden parts of the building were destroyed, the bell tower was ruined, and the carved iconostasis was destroyed.

In Soviet times, the church was inactive and used as a bookbinding workshop. In 1960, it was placed under state protection as a monument of federal significance. In the mid-2000s, the church was returned to the Russian Orthodox Church, and in 2008, services resumed there.