Making use of the effective field theory (EFT) and a cutting approximation, in the framework of Ising model, we investigate the thermodynamic properties of a random transverse mixed spin system with a crystal field. Special emphasis is placed on the influence of crystal field, transverse field and random concentration on phase transitions of the system. Our studies find that a smaller crystal field cannot change the percolation threshold of the critical transverse field in the presence of a random transverse field, and that the reentrant phenomena shall appear in the range of random concentration concerned when the transverse field takes a larger value, where as the reentrant phenomena do not occur and when the transverse field takes a smaller value. These new thermodynamic properties have not been reported in previous works so far as we know. We give a series of pha se diagrams and discuss them in detail.