Harris County Sheriff's Office investigators said the woman's family called at about 10 a.m., concerned they hadn't heard from her in some time. Deputies found the couple a short time later in the vehicle.
The man and woman were both dead from apparent gunshot wounds.
Relatives told authorities the couple had been going through marital issues and family members feared it could result in violence.
The couple, who relatives say have four children together, lived just a couple of miles from the spot where they were found.