A type of limit order to buy or sell shares near the market close only if the closing price is trading better than the limit price. This order is an expansion of the market-on-close order, adding to it a limit condition, which places a maximum on the entry price and minimum on the selling price.
Taobiz explains Limit-On-Close Order
Say a trader believes that, because of increased volume, the best price he or she will receive is at the market close - the trader might then enter a market-on-close order. But if the trader does not want to face an unpredictable entry price, he or she will enter a limit-on-close order. For example, if the trader entered a buy limit-on-close order for 100 shares of ABC at $52.50 and the shares at the end of the day traded at $50, the order would be executed. If, on the other hand, the price rose to $54 right at the end of the day, the order would not be filled.
