NEW YORK — One of the nation’s largest pension funds says it will vote its 5.3 million shares against all of Walmart’s board nominees — including the company’s current and former CEOs — at the retailer’s annual meeting next week.

The California State Teachers’ Retirement System, known as CalSTERS, said Tuesday that it has lost faith in the board’s independence amid allegations of bribery in operations in Mexico.

Along with CEO Mike Duke and former CEO Lee Scott, Walmart’s nominees to the board include 15 incumbents and a new candidate who is a Google Inc. executive.

The pension fund filed a lawsuit in early May seeking changes in corporate governance and improvements in internal procedures at the world’s largest retailer.

Last week, two leading independent proxy advisory firms, ISS and Glass Lewis & Co., separately recommended that Walmart shareholders vote against certain board members, including Duke and Scott.

Early this month, New York City comptroller John C. Liu said the five city pension funds he advises will vote against five board members. The New York City Pension Funds own 5.6 million shares of Walmart, slightly more than CalSTERS.

In late April, The New York Times reported that Wal-Mart allegedly failed to notify law enforcement after its own investigators found evidence that $24 million in bribes was funneled through its Mexican unit in the hopes of speeding permits.