The tragedy happened at about 6:50 p.m. in the 800 block of Volney.
When first responders arrived at the scene, they found the boy unconscious and attempted to treat him. He was rushed to Mainland Medical Center in Texas City, where police said he died.
Police said a large party was being hosted that evening at the rental house, which has a pool.
The Galveston County Medical Examiner's Office confirmed that the boy who died was Joseph Boyd, who turned 6 years old in June.
Police are trying to determine what led to the boy's drowning and who - if anyone - was watching over the pool when Boyd went under the water.
It is unclear how long the boy had been underwater before anyone noticed, Lt. Forrest Gandy said.
While the criminal investigation division of the La Marque Police Department is looking into the matter, it doesn't mean that police believe a crime took place. Anytime a child dies before they are supposed to, we are going to investigate, Gandy said.
Police confirmed that the house is a known party spot within the city and has been a hot spot for noise and disturbance complaints for years.
Police are also trying to determine if, given the size of the gathering and the fact that the house was rented out for a party, the city's ordinances regulating mass gatherings were followed.
Gandy confirmed that such an event would typically require a permit, but no permit exists for the event over the holiday.
In addition to permits, such events may be subject to rules that require law enforcement or first responders to be at the location.
Joshua Pritchett, the city's public relations officer, confirmed that the city does not have a short-term rental ordinance.
The drowning isn't the first involving a young child at that house during a party.
In 2014, a 4-year-old girl drowned while attending a birthday party at the house.
Court records show the girl's family sued the house owner claiming negligence in drowning.
A jury found the homeowner was not negligent or at fault.
County property records show that the house owner is the same person who owned the property when the 2014 drowning occurred.
An investigation is underway but police are urging anyone with information on the incident to contact Lt. Gandy at 409-938-9235.