The ex-serviceman won gold in the first event in Park City, USA and claimed silver in the second in Iglis, Austria.
But the 28-year-old lost to America’s Eric Eierdam by just 0.01 seconds in the final event in Switzerland.
“The first ever World Cup has been truly unbelievable,” said Richardson. “I am thrilled to come second.”
However, the sport and Para-bobsleigh will not be part of the Winter Paralympic schedule until at least 2022.