Eastern Bank plans to continue Century Bank’s marijuana-banking business once it acquires its competitor later this year, Eastern’s chief executive said Thursday.

Century (Nasdaq: CNBKA) was the first Massachusetts bank to accept deposits from marijuana-linked businesses and, despite the growth of the state’s cannabis sector, remains one of only a handful willing to do so today. Even though recreational and medical marijuana use is legal in Massachusetts, it remains illegal at the federal level, creating complications and uncertainty in a banking industry that is known for its aversion to risk.