A manhunt is underway after a random stabbing attack on an Inner West Sydney bus left a 51-year-old man with wounds to his arm and hand.

Police are searching for a man following the assault which occurred just before 1am on Thursday.

Emergency services were called to Addison Road, in Marrickville, following reports of a stabbing.

On arrival, officers were told the man in his 50s had been stabbed by another man who had left the scene after getting off the bus.

"The two men on the bus were not known to one another," a NSW Police spokesperson told SkyNews.com.au.

The stabbing victim was treated at the scene by paramedics before being taken to Royal Prince Alfred Hospital in a serious but stable condition.

Police established a crime scene and commenced an investigation into the incident.

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