Police rushed to the scene after receiving reports of an incident shortly before the evening rush hour.
They arrived at the station with ambulance crews to find two men suffering from stab wounds.
A witness said it appeared a chase had happened due to the distance between separate crime scenes, with an alley also closed off.
A double stabbing has sparked a major police operation outside Victoria Station
He said: “I came out of the station and things were calm inside but there were some youths being held by Met police outside and an increasing number of police cars were arriving.
Bloody clothing at the scene of the attack this evening
"A medical team was attending to a man sitting down on a stretcher but he was conscious and speaking to an officer.
"It seems like there may have been a chase going on because the crime scene was split in these two locations."
Police at the scene of this evening's stabbing
A Scotland Yard spokesman said: "Police were called at around 16:20hrs on Tuesday, 7 March to reports of a stabbing in Wilton Road, SW1.
"Officers and London Ambulance Service attended and found two males with stab injuries.
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"They have been taken to a central London hospital. We await an update on their condition.
Police rushed to the scene following the double stabbing this afternoon
"There have been no arrests and enquiries continue."
Wilton Road has been sealed off at the junction with Victoria Station. A nearby alley has also been sealed off.