Graver Park was created by the Ridge Park District, one of 22 independent park boards consolidated into the Chicago Park District in 1934. Between 1920 and 1930, the population of the Ridge Park District's fashionable Beverly neighborhood increased by nearly 80%. To meet the recreational needs of those living in the southeast corner of its territory, the Ridge Park District began to purchase land there in 1928 and continued until 1931 when streets and alleys were vacated for park expansion.  After the Chicago Park District acquired the park in 1934 when the 22 park districts were consolidated, it added many outdoor athletic facilities. Though land acquisition continued through 1935, the district almost immediately decided to build a fieldhouse in the new park. Designed by Hetherington & Sons, Architects, and completed in 1929, the yellow brick fieldhouse had an assembly hall, three small club rooms, and two banquet halls. The following year, the Beverly-based Hetherington firm designed a shelter house and laid out a landscape plan for the park. The most recent improvement is an interactive waterplay area, constructed in 1998 when the Chicago Park District acquired more land for park expansion.

Though the 1929 park dedication program referred to the site as "Geringer Park," this never became its official name. At a park board meeting the following month, only Board President John Geringer voted in favor of that name. The park was variously known as Church Street Park (for an adjacent street) and Park No. 179 until the early 1950s, when the Chicago Park District designated the site Graver Park. The name honors Beverly resident and Chicago Park Commissioner Philip S. Graver (1878-1945). An official of the Graver Corporation, a producer of steel plate, Graver served on the South Park Board between 1928 and 1934. He was named commissioner of the Chicago Park District in 1936, and served as its vice president from 1937 until his death in 1945.

Located in the East Beverly/Morgan Park community area, Graver Park totals 4.97 acres and features an auditorium, science lab, woodshop and a multi-purpose room. Outside, the park offers a water park, tennis courts, playground, softball, baseball, and soccer fields.

Park-goers can participate in seasonal sports, lacrosse, arts & crafts, gymnastics, young scientist, woodcraft, model car making, and Moms and Tots. On the cultural side, Graver Park offers Park Voyagers. Nature programming that is offered includes Garden Buddies. After school programs are offered throughout the school year, and during the summer, youth can participate in the Chicago Park District’s popular six-week day camp.

In addition to programs, Graver Park hosts fun special events throughout the year for the entire family, such as holiday themed-events.