The least square value for classical cooperative games provides a kind of least square optimization method of allocating benefits to the players, which minimizes the expected deviation between the payoffs and the worths of all coalitions. This paper constructs an optimization model for the least square value of cooperative games in which cooperation among players is based on a set system of feasible coalitions. The existence and uniqueness of the least square value are investigated on the basis of the convex programming theory. Meanwhile, an equivalent matrix equation for solving the least square value is obtained by using the Lagrange multiplier method, and then, based on this equation, the expression and several important properties of the value are discussed. Besides, the so-called symmetric least square value is proposed by employing a distribution rule that the inseparable players gain the same payoffs, and its properties are also studied. It is worth noting that the class of cooperative games with feasible coalitions has a unique least square value if and only if the rank of the set of feasible coalitions is full. These results can provide theoretical perspective and decision-making reference for distributing the worth of players when not all coalitons can be formed.