The Spaniard was the fastest race driver on an overcast and humid opening day dominated by compatriot Pedro de la Rosa in the third McLaren.
"I think they (McLaren) are a little bit stronger than us...but here it will be very close between the two teams I hope," said Alonso, who enjoys a 32-point lead in the championship.
De la Rosa, the reserve who will not compete in Sunday's eighth round of the championship, topped the timesheets in both hour-long sessions ahead of Toyota's Brazilian test driver Ricardo Zonta.
Alonso, who did not set a time in the morning to save his car for the afternoon, did 33 laps and was third quickest with a lap 0.714 off De la Rosa's time of one minute 14.662 seconds.
McLaren's Kimi Raikkonen, Alonso's closest rival in the battle for the title along with Toyota's Italian Jarno Trulli, was the fastest race driver in the morning.
"I'm still not 100 percent happy with the set-up of the car but we can work on that," said Raikkonen.
The Finn, who crashed out on the final lap with suspension failure while leading the European Grand Prix at the Nuerburgring last month, was fifth in the afternoon at Montreal's Circuit Gilles Villeneuve.
Briton Jenson Button raised BAR's hopes of scoring their first points of the season with the fourth best time in the morning and seventh in the second session.
The 25-year-old said he would be shocked if the Honda-powered team did not score on Sunday, even if Renault and McLaren were clearly ahead of the rest after dominating the season so far.
"It's been good because we've been able to do a lot of laps," he said. "It's been a good day for us and our pace is reasonable."
Ferrari's seven-times world champion Michael Schumacher, without a win since October, went well in the morning with the fifth best time, 0.457 slower than De la Rosa, but was only 16th in the afternoon.
"We are not looking too competitive here, looking at the lap times," said the German.
Schumacher is eighth in the championship, with 16 points, and his hopes of an unprecedented eighth title are looking increasingly slim.
He has, however, won more frequently than any driver in Canada and can become the first in Formula One history to win the same event eight times.
American Scott Speed made his debut at a grand prix weekend as Red Bull's non-racing third driver but his second session was cut short when he skidded off.
"We will be analysing his incident and will be analysing the data we get from his car," said technical director Guenther Steiner. "At the moment the overriding factor is that we're not fast enough."