This school, previously known as Denver Avenue Elementary, was one of a series of schools built in the city between 1909 and 1911. Its original name was the 15th District School. By then, the wards were renamed districts. It was constructed to serve the rapidly growing north side community following the arrival of the Swift and Armour Meatpacking Plants. The original building was rectangular in plan and was two stories on top of a concrete basement. The two main floors were clad in polychrome brown brick with cast stone details and a slightly projecting entrance bay with a decorative parapet and arched entry door. It was designed by Waller and Field and built by the Texas Building Co. In 1926, wings were added on the north and south sides of the building, giving it an "H" shape. In 1936, an auditorium was added behind the south wing, giving the building an "L" shape. In 1979, a cafeteria addition was built to the south and a classroom wing was added in 1989, giving the building its current "U" shape. All of the additions were similar in design to the original school building. Accessibility issues were addressed at the school in 2003, when an elevator was added on the north side of the building. The school was renamed for Rufino Mendoza, Sr., a north side postal carrier.