Spectrum sensing in a wideband regime for cognitive radio network (CRN) faces considerably technical challenge due to the constraints on ADCs, especially in the presence of primary user emulation attack (PUEA) where some malicious users try to impersonate the primary user (PU) to prevent other secondary users (SUs) from accessing the idle spectrum. To address this issue, an eigenvalue-based compressive wideband spectrum sensing (ECWSS) scheme is proposed in this paper. ECWSS directly utilizes the compressive measurements based on compressive sampling (CS) theory to perform wideband spectrum sensing without requiring signal recovery. In ECWSS, the sensors around a SU carry out compressive sampling at the sub-Nyquist rate instead of the SU. Furthermore, the exact probability density function of extreme eigenvalues is used to set the threshold. Theoretical analysis and simulation results show that compared to the traditional sensing scheme, ECWSS has better detection performance and is more robust in the existence of PUEA.