He joined Coloni's Grand Prix team for 1988, having driven for them in F3000 in 1986. The season saw a prequalifying system being put in place as there were 31 entrants for a maximum 30 places in qualifying proper. As such, the slowest of the new entrants for the season (Coloni, Rial, Dallara and EuroBrun) would be eliminated from proceedings after the Friday morning session regardless of their overall position - Tarquini failed to prequalify several times despite often being faster than some of the exempt entrants (such as the Osella and Zakspeed cars). He drew good notices for his performance overall, however - his 8th place at the Canadian Grand Prix would stand as the team's best ever result and his eight starts the most ever garnered by a Coloni driver.