The Dutch driver was 0.768 seconds quicker than Mexican teammate and closest rival Sergio Perez in the first session and then 0.170 faster than Aston Martin's Alonso in the late afternoon.
Alonso's 32nd and last win was at the same circuit a decade ago with Ferrari and his form at the age of 41 - with five podiums in six races including second in Monaco last weekend - has fired up the fans.
Verstappen's fastest lap around Barcelona's Circuit de Catalunya was a one minute 13.907 second effort on soft tyres in practice two, with Alonso clocking 1:14.077.
The circuit has been shortened slightly, with the final chicane no longer used, and returned to a layout last used in 2006.
Verstappen, who took his first F1 win at the circuit in 2016 and also won last year, leads closest rival Perez by 39 points after winning four of six races. Red Bull have won all six.
Alpine's Esteban Ocon, fresh from third place in Monaco last Sunday, was best of the rest in practice one while Haas's Nico Hulkenberg was third in the second session with Perez fourth and Ocon fifth.
Ferrari introduced a new look upgraded car but Charles Leclerc and Carlos Sainz were eighth and ninth with Mercedes' George Russell, who had been trying out prototype Pirelli tyres for much of the session, 10th.
Leclerc ran the old design and Sainz the new bodywork as Ferrari conducted a comparison.
The top teams were all running with sensors and fluorescent 'flow-vis' paint early in the session as they sought aerodynamic data.
Several drivers also complained about the bumpy approach to the final corner.
