The accident happened at 5pm on Wednesday at Kalitola area.
The deceased were identified as school teacher Anisur Rahman, 31, his mother Rehena Begum, his wife Razia Sultana and Razia’s brother Jahid.
Local sources said the family met the tragic end of their life while returning home after visiting a doctor.
Seven others were also injured in the accident. Of the, crititcally injured four were admitted to Rangpur and Bagura Medical College Hospital.
Gabindaganj Highway Police Station OC Khairul Islam said police seized the covered van but its driver managed to flee the scene.