This paper investigates the global asymptotic synchronization in an array of coupled neural networks with random coupling strengths, probabilistic interval time-varying coupling delays as well as unbounded distributed delays (mixed delays). Two important integral inequalities that include the Jensen's inequality as a special case are developed. On the basis of the developed inequalities, the properties of random variables and Lyapunov functional method, several delay-dependent sufficient synchronization criteria are derived for the considered model. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using MATLAB LMI Toolbox. Some existing results are improved and extended by taking different values of parameters of the obtained results. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.