The paper studies finite-time quasi-synchronization (FTQS) for time-delay multilayer networks (MLNs), the FTQS of MLNs is achieved by applying delay controller. Compared with some existing results, the optimal combination relevance between exponential power of FT controller and initial value of system is gained when the QS time is minimal. In particular, there is no necessary correlation between the FT convergence of the system and the range of QS error. Lastly, the validity of the advanced method is verified by FTQS simulation of MLNs with financial oscillators.