We present a spectral analysis of the black hole candidate and X-ray transient source Swift J1753.5 0127 making use of simultaneous observations of XMM-Newton and Rossi X-ray Timing Explorer (RXTE) in 2006, when the source was in outburst. The aim of this paper is to test whether a thermal component due to the accretion disc is present in the X-ray spectrum. We fit the data with a range of spectral models, and we find that for all of these models the fits to the X-ray energy spectra significantly require the addition of the disc black-body component. We also find a broad iron emission line at around 6.5 keV, most likely due to iron in the accretion disc. Our results confirm the existence of a cool inner disc extending near or close to the innermost circular orbit (ISCO).We further discovered broad emission lines of NVII and OVIII at ~ 0.52 keV and 0.65 keV, respectively in the RGS spectrum of Swift J1753.5-0127.