A novel L-band slow wave structure (SWS) for compact and high-efficiency relativistic Cerenkov oscillator is proposed. The SWS is composed of orthogonal array of two all-metal metamaterial units. Since the metamaterial used for constructing the SWS has a negative equivalent permittivity and permeability, the fundamental mode of the SWS has a negative dispersion and can work below cutoff frequency of circular waveguide with the same size, indicating that the structure has advantage of miniaturization. Analysis of high-frequency characteristics shows that interaction impedance of the fundamental mode (quasi TM01 mode) is greater than 70 Ω across operating frequency band, which indicates that this structure is expected to achieve the high efficiency of high power microwave sources. By adopting an orthogonal arrangement between metamaterial resonant units, the angular uniformity of electric field in SWS space is significantly improved, and the non-uniformity of electric field due to asymmetry of the metamaterial units is reduced. In addition, an L-band relativistic Cerenkov oscillator is constructed using this metamaterial SWS. In the acceleration voltage U = 550 kV, beam current I = 1.5 kA, and axial uniform magnetic field B = 1.5 T conditions, preliminary particle simulations show that the Cerenkov oscillator obtains a 240 MW average power at 1.405 GHz, with an efficiency of 29.1%, and axial length around one λ. This Cerenkov oscillator obtains a high power and efficiency in a miniature and compact microwave device.