Spectral properties, both the optical spectrum and the intensity noise spectrum, of a broad-area diode laser with off-axis external-cavity feedback are presented. We show that the optical spectrum of the diode laser system is shifted to longer wavelengths due to the external-cavity feedback. The intensity noise spectrum of the diode laser shows that the intensity noise is increased strongly by the external-cavity feedback. External-cavity modes are excited in the external cavity even in the off-axis configuration. The peak spacing of the intensity noise spectrum shows that single roundtrip external-cavity modes are excited. We believe that the four-wave mixing process in the broad-area diode laser is responsible for the establishment of the external-cavity mode.