A man is clinging to life after he was shot in the back of the head in a broad-daylight attack on a busy Brooklyn street near the Botanical Garden and Brooklyn Museum, cops said. 

The victim, believed to be in his 30s, was shot around 4:15 p.m. on Franklin Avenue near Lincoln Place in Crown Heights — steps from the Franklin Avenue-Medgar Evers College subway station, police said. 

He was rushed to the Kings County Hospital Center, where he was listed in critical condition, police said. 

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One person fled on foot following the brazen crime, cops said. No arrests have been made. 

The motive for the late afternoon violence remains under investigation.