The trace norm of matrices plays an important role in quantum information and quantum computing.How to quantify it in today\'s noisy intermediate scale quantum (NISQ) devices is a crucial task for information processing.In this paper,we present three variational quantum algorithms on NISQ devices to estimate the trace norms corresponding to different situations.Compared with the previous methods,our means greatly reduce the requirement for quantum resources.Numerical experiments are provided to illustrate the effectiveness of our algorithms.