Witnesses have been asked to come forward after the incident on platform three at Ealing Broadway station on November 24, at 12.07am.
The train departed while the passenger’s hand was still trapped in the doors, before they were pulled clear by a member of staff.
The Rail Accident Investigation Branch (RAIB) said: “The passenger, who had been attempting to board the train, was forced to run alongside it for several metres before being pulled away by a member of railway staff who was working on the platform.”
At the time, the driver was alerted to what was happening by passengers and the train was stopped after moving 17 metres.
The passenger is reported to have sustained minor injuries.
A safety investigation has launched to determine the sequence of events.
Anyone with information is asked to call 01332 253324 or email witness@raib.gov.uk.