The new state-of-the art school will provide non-denominational primary education for up to 462 primary and 128 nursery pupils when complete in 2022.
The steel framework is already in place after the start of construction was delayed until June 2020 due to the covid-19 outbreak.
The new school is required to cope with increasing demand in the growing Calderwood Core Development Area, which is expected to see 2,400 new homes completed in the area as well as associated infrastructure improvements.
Executive councillor for education David Dodds said: "Excellent progress is being made to build the new Calderwood Primary.
"The design of the new state-of-the art school incorporates elements of the award-winning West Calder High School, with sustainability and suitability as core objectives.
"Calderwood Primary will provide an anchor landmark for the Calderwood Core Development Area when it opens, helping bring the new community at Calderwood together."
The project is being delivered on behalf of the council by its development partner Hub South East, with Morrison Construction as the primary contractor. This is the same team who have a strong track record with new schools, with the successful delivery of the award-winning West Calder High School.
Scott Brown, Hub South East's Project Director said: "It's fantastic to see the new Calderwood Primary School really taking shape. Work on site is progressing well and we look forward to delivering this new learning space for West Lothian Council, ensuring that a range of community benefits and social value are realised for the local community during construction."
Eddie Robertson, Managing Director for Morrison Construction Building Central, commented: "The team at Calderwood are making excellent progress following the delayed start on site and I thank them all for their efforts. We will be pressing ahead to continue that progress in conjunction with all the stakeholders in order to deliver a first-class facility for local children in 2022."
Stirling Developments are the lead developer and master planners for the Calderwood development.
Peter Stirling, Managing Director for Stirling Developments, added: "Having been involved in the design and delivery of Calderwood since 2004, we are delighted that primary school will activate the village square and deliver a community facility we can all be proud of."