The founder and chief executive of a troubled charter-school network in Brooklyn was accused by state prosecutors Thursday of repeatedly failing to pay income taxes and creating phony records.

Eddie Calderon-Melendez, the CEO of the Believe High School Network, failed to pay taxes on more than $1.4 million in compensation between 2005 and 2010, Attorney General Schneiderman said in a statement announcing the indictment. During that period, Calderon-Melendez allegedly never filed a tax return.

Calderon-Melendez...