The emission from the accreting black holes (BHs) in low-mass X-ray binaries (LMXBs) covers a broad energy band from radio to X-rays. Studying the correlations between emission in different energy bands during outbursts can provide valuable information about the accretion process. We analyse the simultaneous optical, ultraviolet (UV), and X-ray data of the BH-LMXB Swift J1753.5-0127 during its similar to 12-yr long outburst with the Neil Gehrels Swift Observatory. We find that the UV/optical and X-ray emission are strongly correlated during the hard states of the outburst. We fit the relation with a power-law function F-UV/optical proportional to F-X(beta) and find that the power-law index beta increases from similar to 0.24 to similar to 0.33 as the UV/optical wavelength decreases from similar to 5402 angstrom (V) to similar to 2030 angstrom (UVW2). We explore the possible reasons for this and suggest that in Swift J1753.5-0127 the UV/optical emission is dominated by a viscously heated accretion disc at large radii. We find that the data that deviate from the correlation correspond to the low-intensity peaks appeared in the X-ray band during the outburst, and suggest that these deviations are driven by the emission from the inner part of the accretion disc.