Officers said a 39-year-old man had been walking on a pathway close to Buchanan Crescent in the town when he was approached and threatened by a male teenager with a knife.
The suspect, believed to be between 13 and 15 years old, then stole a small amount of cash and fled from the scene.
The youth was also described as wearing a pale blue scarf and a dark blue hooded top.
Officers described the incident as "frightening" and called on any witnesses to come forward with information.
Detective Constable John Irvine at Livingston CID said: “Thankfully the man was not injured, however, to be threatened with a knife, was very frightening for him. All this for only a few pounds.
“The path is used by locals to walk their dogs or for going to the nearby supermarket, so at this time of the evening, it’s possible that someone may have seen the boy hanging about the area or running off towards the bridge at the train track shortly afterwards.
“Anyone with information can call Livingston CID via 101. Please quote reference number 3155 of Saturday 19 October, 2019, when calling. Alternatively, Crimestoppers can be contacted in confidence on 0800 555 111."