Massive multiple-input multiple-output (M-MIMO) technology is considered to be a key enabling technology for future wireless communication systems. One of the challenges in effectively implementing an advanced precoding scheme to a large-scale array antenna is how to reduce the mutual coupling among antenna elements. In this paper, a new concept that is called array-antenna decoupling surface (ADS) for reducing the mutual coupling between antenna elements in a large-scale array antenna is proposed for the first time. An ADS is a thin surface that is composed of a plurality of electrical small metal patches and is placed in front of the array antenna. The partially diffracted waves from the ADS can be controlled to cancel the unwanted coupled waves. Two practical design examples are given to illustrate the design process and considerations, and to demonstrate the usefulness of ADS for the applications of phased array antennas and M-MIMO systems when commonly used precoding schemes are applied. The attractive features of ADS include its applicability to a large-scale array antenna; suitability for a wide range of antenna forms; wide decoupling bandwidth; and simplicity in implementation.