St Matthew's Church of England Primary School on Windmill Lane will go from a 210 place school to offer 420 places to children from age four to 11.
The new building is over the road from the school on Croxall Way and will accommodate the older children once finished.
Councillor Joyce Underhill, cabinet member for best start in life, was shown around the new building by St Matthew's pupils who are members of the school council.
She said: "I thoroughly enjoyed my visit to the school and it was an absolute pleasure to be shown round by the children.
"The extension to the school is coming along very well and these extra 210 primary school places helps make sure we keep up with demand from families in Sandwell. I look forward to seeing the building finished in the coming months.
The new building will include seven classrooms, a specialist teaching classroom, two group rooms, library, hall, kitchen, a multi-use games area and outdoor teaching areas.
Fiona Deakin, headteacher at St Matthew's, said: "This is a wonderful opportunity for everyone at St Matthew's and we are excited to move into the new KS2 building.
"By having a split site, we will be able to retain all that is distinctive and special about a small school whilst tailoring the space to serve the needs of our children as they move through their primary school years."
The £4.4million extension is being constructed by Local West Midlands construction firm A M Griffiths & Son Ltd.
Brendan Oakley, business development director at A M Griffiths & Son Ltd, said: "The new school building is being constructed to an agreed design using AMG’s own unique and innovative RoWeRS method of construction.
"The council and the school are a great client to work with and the site team are very enthusiastic about getting them involved with the build at every opportunity."
The building is due to be completed in early 2020 ready for staff and pupils to move into as soon as possible after the hand-over of the building.