Real-time data-intensive applications with security concerns are arising in many disciplines of science and engineering. Scheduling algorithms play an important role in the design of real-time data-intensive applications. However, conventional real-time scheduling algorithms are inappropriate to fulfill the security requirements of real-time data-intensive applications. In this paper we have proposed a security-attentive dynamic real-time scheduling algorithm named SARDIG for scheduling real-time data-intensive applications. We have proposed a grid architecture which describes the scheduling framework of real-time data-intensive applications. In addition, we have introduced a mathematical model for providing security of the real-time data-intensive applications and a security gain function to quantitatively measure the security enhancement for applications running in the grid sites. We have also proved that the SARDIG algorithm always provides optimum security for real-time data-intensive applications. The time complexity of the SARDIG algorithm has been analyzed to show the efficiency of the algorithm. Simulation results show that the SARDIG algorithm provides better performance and security than other existing scheduling algorithms. Copyright © 2011 John Wiley & Sons, Ltd.