"Recover health" in Engpsh is commonly expressed as "to regain one's health" or "to recuperate".
The phrase "regain one's health" comes from the verb "to regain", which means to get back something that was lost, and the noun "health", which refers to the state of being free from illness or injury.
Examples:
After a long period of illness, Jane finally regained her health.
(经过长期的生病之后，简终于恢复了健康。)
He needed a few months to recuperate after his surgery.
(他需要几个月的时间来恢复健康。)