Contractor Taylor Woodrow has erected the primary frame and lifted the glass canopy and is now making headway with the terraces underneath.
The Arup designed primary frame consists of four large timber-clad steel columns and beams.
Nine glass canopies are hung from the main frame and are inclined at different angles.
"The structure acts a giant portal frame in two directions,” said Arup associate director Ed Clark.
"The difficulty was the position of the canopies - they sail out beyond the frame and need to be held in position at an angle."
The Serpentine Gallery Pavilion is a fully accessible public space in the Hyde Park, attracting up to 250,000 visitors every Summer and is accompanied by a programme of public talks and events.