He was the eldest surviving son and heir of Sir William Gostwick, 1st Baronet and the former Jane Owen.
His father was created a baronet of Willington, in the County of Bedford, on 25 November 1611 by King James I.
[1] His paternal grandparents were John Gostwick of Willington, Bedfordshire, and the former Elizabeth Petre (a daughter of Gertrude Tyrrell and Sir William Petre, Secretary of State to Kings Henry VIII, Edward VI and Queen Mary I).
[2] After his grandfather's death in c. 1582, Elizabeth married Edward Radclyffe, 6th Earl of Sussex.
[8] Through his son Edward, he was a grandfather of Sir William Gostwick, 4th Baronet, who served as MP for Bedfordshire from 1698 to 1713.