The New York Yankees third baseman, coming back from hip surgery in January, hit a ball to the base of the center-field fence and another on the warning track in left center off a minor league right-hander Monday as he continued taking simulated at-bats.
In sessions late last week, A-Rod primarily hit grounders mixed in with a couple liners.
Rodriguez also had an extensive baserunning session and did sliding drills on a mat in the outfield, two key steps before starting a minor league rehab assignment.
The Yankees have not said when Rodriguez will begin playing in games, but are hoping for after the All-Star break.
A-Rod, the highest-paid player in Major League Baseball this year, is in the midst of a $275 million, 10-year contract with the Yankees that runs through 2017.
He began his major league career with the Seattle Mariners from 1994 to 2000 before moving on the play for the Texas Rangers and then the New York Yankees.