In this study, an investigation was undertaken to research the use of holographic phase masks (HPMs) in photo-thermo-refractive (PTR) glass as mode converters for linearly polarized (LP) fiber modes. A Spatial Light Modulator (SLM) was used to generate higher-order transverse fiber modes LPm,n. Under proper incidence condition on the holographic device, LPm,n modes are diffracted and simultaneously converted into higher order or lower order LP modes. The process was analyzed by imaging the far field on a CCD camera. It is demonstrated that using this novel method of converting transverse fiber modes several combinations of LP modes can be converted to each other with mode conversion efficiencies up to 70%. Mode purities were found to be around 85% for up conversion and around 90% for down conversion, respectively. It is noticed that this approach has several promising applications such as mode multiplexing, beam cleaning and power scaling of higher-order mode fiber lasers and amplifiers by combining mode conversion and beam combining.