Mr. Willis, who was a top executive at Coca-Cola Co.'s Latin American operations, was hired as Kmart's chief marketing officer last fall. He was not available for comment.
Kmart's chairman and CEO, Chuck Conaway, in a brief statement said, "We understand and respect Brent's decision to put his family first and are thankful for his many contributions to Kmart. We wish him well in his new endeavors."
The spokeswoman said Mark Schwartz, Kmart's new president and chief operating officer, will head up marketing and advertising responsibilities for the time being.
The spokeswoman said that it is being evaluated as to whether the position of chief marketing officer will be filled.
Kmart's longtime vice president of advertising, Larry Davis, also remains in the department, the spokeswoman said.