Process monitoring, especially fault diagnosis, is an indispensable component in terms of process safety and profit. Since transfer entropy as a data-driven technique for fault diagnosis was proposed in the early 2000s, many attempts for application to chemical processes were reported. However, the application was limited because it requires high computational cost owing to the increased complexity and scale of chemical processes. This paper proposes an integrated transfer entropy method with the graphical lasso, a regularized optimization method for relevant subset selection. The proposed methodology exploits the outstanding performance of transfer entropy in diagnosis while mitigating the disadvantages in terms of the computational cost via the graphical lasso. To illustrate the effectiveness of the proposed method, two case studies were carried out. The SCR system, a catalytic after-treatment system for automobile exhaust gas, was examined to verify the feasibility of the proposed method. Then, the Tennessee Eastman process, which is a benchmark process, was also tested as a representative of the industrial-scale chemical process. The results of the proposed method demonstrate that in all cases it significantly reduces the computational cost of root cause analysis using transfer entropy, and even outperforms the conventional transfer entropy method for diagnosis in some particular cases.