"I am quite happy with the first testing day of our new car," the German told Ferrari's official website after the session at Fiorano. "I immediately had a feeling for it."
"The F2004 was handling very well straight out of the box and we achieved good and consistent lap times."
Ferrari, seeking their sixth successive constructors' championship this season, launched the new car at a snowy Maranello on Monday.
Team bosses said at the time that some key parts, mainly aerodynamical, were not yet ready and the car would look very different when the season starts in Australia on March 7.
Schumacher, winner of a record sixth title last year, tested the old F2003-GA in Valencia earlier in the week and returned to Italy on Thursday for the new car's first run.
While no official times were given for the session behind closed doors, Italy's Gazzetta dello Sport website reported that the car had gone faster than any other Ferrari on its debut.
It said the F2004 had lapped in 56.835 seconds while last year's F2003-GA clocked a best lap on its debut last February of 57.045.
