This paper studies an M/G/1 queueing system with a patient server and uninterrupted multiple vacations under the control of ($ p, N$)-policy. In which, when the system becomes empty, the server goes on a uninterrupted vacation, and when the server returns from the vacation and finds at least $N( {N \geqslant 1} )$ customers in the system, the server immediately starts serving until the system becomes empty again. If there are customers but less than $N$, then the server starts serving with probability $p\, ( {0 \leqslant p \leqslant 1} )$, or waits with probability $ {1 - p} $ until $N$ customers are reached. We first apply the stochastic decomposition property of the steady-state queue size to derive its probability generating function and the average queue size. Also, the average waiting time of an arbitrary customer is obtained using the Little’s formula. Finally, we establish the cost structure model of the system and use the renewal reward theorem to derive the explicit expression of the long-run expected cost per unit time of the system. Furthermore, the cost optimization problems with (without) the expected waiting time constraints are respectively discussed. Numerical examples are provided to determine the one-dimensional optimal control policy $N $* that minimizes the system cost as well as the two- dimensional optimal control policy ($N $*, $ T$*) when the vacation time is a fixed time length $T $.