The platforms sit on an embankment slightly above ground level and crosses above the Bay Ridge Branch of the Long Island Rail Road.

The Brooklyn, Flatbush and Coney Island Railway (BF&CI; now the BMT Brighton Line) opened in 1878.

[7] The BF&CI was reorganized as the Brooklyn and Brighton Beach Railroad in 1887[8]: 91 [9] and was subsequently leased by the Kings County Elevated Railway (KCER) in 1896.

"[3]: 3 In 1906 Ackerson built a real estate office on the southwest corner of East 15th Street and Avenue to sell homes in their development.

[3]: 3 The sales office was converted to railroad use and "debuted as a transit station" on August 23, 1907,and was renamed "Avenue H".

[3]: 3 [17] In this same time frame, the Brighton Beach Line was rebuilt as a four-track railroad and regraded from Church Avenue to Sheepshead Bay.

This rebuilding placed the Avenue H station at the transition point between the open cut to the north and the embankment to the south.

On August 1, 1920, a tunnel under Flatbush Avenue opened, connecting the Brighton Line to the Broadway subway in Manhattan.

[3]: 3 In 2003, the Metropolitan Transportation Authority announced plans to demolish the station house, citing its wood construction as a fire hazard.

[26] Northbound accessibility for this station was proposed in February 2019 as part of the MTA's "Fast Forward" program.

[28] The work started in October 2020 and necessitated minor service diversions; it also created a park at the dead-end on Avenue H west of East 16th Street.

To facilitate the construction of an accessible wheelchair ramp, the northbound platform was closed for renovations during March and April 2021.

[33] Plans for the Interborough Express, a light rail line using the Bay Ridge Branch right of way, were announced in 2023.

[38] The main entrance is the station house on the east side of the tracks, adjacent to the northbound platform on the south side of Avenue H.[39] Designed in a similar Colonial Revival and Queen Anne style to the neighborhood's residences, the station house is one story high and contains wooden shingles on its facade.

The Avenue H facade, along the north side of the station building, consists of four bays with two wood-and-glass doors leading to the fare control area.

[39] Another station house is on the north end of the southbound platform, adjacent to the west side of the track.