"We can't win the championship this year, we're certainly not racing Ferrari head to head everywhere," he told BBC radio on Thursday.
"We're just doing a very good job and we're going to try and get up the championship as far as we can.
"I certainly think that winning one or two races maybe is a strong possibility and its practical for us to set a target of finishing second in the championship," he added.
"That's rather higher than our original target which was to compete with the top three."
Last weekend Briton Jenson Button gave BAR their first pole position and best race result since they entered the sport in 1999 with his own career-best second place in the San Marino Grand Prix.
Button has been the revelation of the early part of the season, racking up three podium finishes in a row and challenging strongly for second place in the drivers' championship behind Michael Schumacher.
The 24-year-old is third, just a point behind Schumacher's Ferrari team mate Rubens Barrichello.
BAR are third equal in the constructors' championship, level on points with Williams and four points behind second placed Renault.
Willis said Button was raising his performance in every race and BAR had a long-term plan to challenge for the championship, with the first stage being to establish that they could win races.
"The second is to establish that you can win very regularly and the third is to establish that you can win every time that you turn up," he said.
The next race is in Barcelona on May 9 with Schumacher chasing his fifth win in a row to equal Formula One's best start to a season.
Willis said the six-times champion could expect to be pushed hard by BAR.
"I think the car, engine, tyre and driver package for BAR is very strong at Barcelona. We've been consistently quick every time we've been to Barcelona since we first ran the hybrid car," he said.
"It ought to be one of our very strong races, not necessarily because the car's got strong circuits and weak circuits but its just one where we've already shown that we're very competitive.
"We'll certainly give it a very hard go ... I'm sure we can be very strong there. We'll certainly aim to be right up at the front end of the grid in qualifying and I believe that we can get on the podium again."
