While Solskjaer has sometimes divided opinion at Old Trafford, United remain in the hunt for a top-four spot in the Premier League and two cup competitions.
Although there has been talk of the Norwegian being replaced in the summer, Beckham feels that his former teammate deserves plenty of praise.
The ex-midfielder told Sky Sports News: "I think he's doing a good job. the fact that he's stepped in and stepped up, and that he continues to be positive about players, he's got that from the boss [Sir Alex Ferguson]. He would never criticise a player from his club and Ole has been exactly the same.
"All of the fans will be behind him because he's a great person and because of what he's done for Manchester United over the years."
Solskjaer has won 36 and lost 19 of his 71 matches in charge in all competitions. body check tags ::