Sanjeev and Sadhana Prasad, 61 and 57, say they used up their savings raising their son, paying for his pilot's training as well as a lavish wedding.
They are demanding compensation worth nearly $650,000 (£525,000) if no grandchild is born within a year.
Their son and his wife do not appear to have commented.
The highly unusual lawsuit was filed on grounds of "mental harassment".
Mr Prasad said he had spent all his savings on his son, sending him to the US in 2006 for pilot training at a cost of $65,000.