The negative imaginary property is a property that many practical systems exhibit. This paper is concerned with the negative imaginary synthesis problem for linear time-invariant systems by output feedback control. Sufficient conditions are developed for the design of static output feedback controllers, dynamic output feedback controllers and observer-based feedback controllers. Based on the design conditions, a numerical algorithm is suggested to find the desired controllers. Structural constraints can be imposed on the controllers to reflect the practical system constraints. Also, the separation principle is shown to be valid for the observer-based design. Finally, three numerical examples are presented to illustrate the efficiency of the developed theory. (C) 2016 Elsevier Ltd. All rights reserved.