To achieve high force output and low mover mass of tubular linear oscillating machines simultaneously, we proposed a novel compound Halbach array consisting of the outer layer of quasi-Halbach array and inner layer of axial magnetized pattern. This magnetic pattern can completely removed the high-density back iron existed in conventional linear PM machines due to the much improvement of self-shielding effect. Thus, the mover mass can be greatly reduced and hence high dynamic performance can be obtain. Firstly, the mathematical models of the magnetic field and force output are established. And then, the key design parameters of the compound Halbach array are extracted from the analytical models. Besides, the response surfaces of force output and thrust fluctuation are established for investigating the coupling effect of these key design parameters on output characteristics. A multi-objective genetic optimization algorithm is performed to obtain structural parameters. Finally, the electromagnetic characteristics of the compound Halbach array are compared with conventional Halbach array to verify its merits.