Ferrari driver Alonso was just 0.012 seconds quicker than Hamilton as Lotus’s Romain Grosjean took third ahead of Red Bull’s Mark Webber and Mercedes’ Nico Rosberg.
“The car feels pretty good and I feel like I’m pretty on it this weekend,” said Hamilton after the second session in Montreal.
“I wouldn’t say it’s a big step forward. I still don’t feel right in the car for some reason. I don’t know if it’s my seat.
“Today I was doing my belts up really tight, which I never do.”
Hamilton added: “I don’t know what the tyres look like in terms of wear, but they’re feeling quite good.
“They [the team] told me to push the last couple of laps which I was able to do as I had the grip.
“But everyone’s going to be in the same boat. I don’t think we’re trouble at the moment.”
1. Fernando Alonso Spain Ferrari-Ferrari 1m 14.818s
2. Lewis Hamilton Britain Mercedes-Mercedes 1m 14.830s
3. Romain Grosjean France Lotus-Renault 1m 15.083s
4. Mark Webber Australia Red Bull-Renault 1m 15.212s
5. Nico Rosberg Germany Mercedes-Mercedes 1m 15.249s
6. Felipe Massa Brazil Ferrari-Ferrari 1m 15.254s
7. Sebastian Vettel Germany Red Bull-Renault 1m 15.280s
8. Adrian Sutil Germany Force India-Mercedes 1m 15.396s
9. Jenson Button Britain McLaren-Mercedes 1m 15.422s
10. Daniel Ricciardo Australia Toro Rosso-Ferrari 1m 15.566s
11. Kimi Raikkonen Finland Lotus-Renault 1m 15.599s
12. Sergio Perez Mexico McLaren-Mercedes 1m 15.661s
13. Paul di Resta Britain Force India-Mercedes 1m 15.855s
14. Pastor Maldonado Venezuela Williams-Renault 1m 16.319s
15. Jean-Eric Vergne France Toro Rosso-Ferrari 1m 16.351s
16. Valtteri Bottas Finland Williams-Renault 1m 16.374s
17. Esteban Gutierrez Mexico Sauber-Ferrari 1m 16.475s
18. Nico Hulkenberg Germany Sauber-Ferrari 1m 16.929s
19. Jules Bianchi France Marussia-Cosworth 1m 17.070s
20. Charles Pic France Caterham-Renault 1m 17.236s
21. Max Chilton Britain Marussia-Cosworth 1m 17.888s
22. Giedo van der Garde Holland Caterham-Renault 1m 18.392s
23. Alexander Rossi America Caterham-Renault 1m 27.143s*