Yes, Gene Kelly directed several films and TV specials.

Kelly's first attempt at directing comes in 1945, with a U.S. Navy training film called Combat Fatigue Irritability. In this short film, Kelly plays a soldier suffering from "combat fatigue" (now called post-traumatic stress disorder or PTSD), who is "jumpy, nervous, combative, and short-tempered."

The U.S. National Library of Medicine praises Kelly's atypical turn in this role:  
Gene Kelly was famously a joyful and athletic dancer, a romantic and sometimes comedic Hollywood star. But there was another Gene Kelly, a dark Gene Kelly, who, in a few films, was especially good at playing morally troubled, and even unbalanced, characters. ​
For those interested in learning more, Kelly's eldest daughter Kerry Kelly Novick, a child psychoanalyst in Michigan, discusses Combat Fatigue Irritability in a three-part interview.
Next, Gene Kelly flexed his directorial muscles in MGM's On the Town (1949). This film, which he co-directed with Stanley Donen, was particularly innovative because it was the first major studio musical to shoot on location. Because of Gene's (and Donen's) persistence, New York City's most famous sites (rather than the usual replicated studio sets) are featured in the film's ground-breaking opening number.

Gene's second shot at co-directing with Stanley Donen was 1952's Singin' in the Rain. This film is held up as a shining version of the American Film Musical and is Kelly's most famous film.

Next comes It's Always Fair Weather (1955), the third and last Kelly-Donen musical. This one features Gene's dance on roller skates.

​In 1956, Gene directed a string of films. He went to France to create, star in, and direct Invitation to the Dance. Unfortunately, this experimental film wasn't as successful as his others, but Gene pressed on with The Happy Road (1957), The Tunnel of Love (1958), Gigot (1960), and A Guide for the Married Man (1967).

When 1969's Hello Dolly came along, Gene was looking for a hit. The Barbra Streisand-helmed musical wasn't widely praised critically and its budget soared, but it was the fifth-highest grossing film of 1969.

Next was The Cheyenne Social Club from 1970.

Finally, Gene directed That's Entertainment, Part II in 1976. Hoping to capitalize on the success of That's Entertainment (1974), this compilation film pulled on nostalgia of the viewers who enjoyed musicals from the golden age of Hollywood.

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