We investigate heat transfer in supercritical steam flowing in a spiral tube by conducting three-dimensional numerical simulations. The current numerical solver has been validated with the existing experimental results, and simulations are performed by varying different geometric parameters of a spiral tube. The flow dynamics and heat transfer in a spiral tube are compared against those in a straight tube. For the parameters range considered in the present study, it is found that the heat transfer coefficient (HTC) in the spiral tube is 29% higher than that in the case of a straight tube for the same flow and thermal conditions. Our results indicate that the tangential velocity component resulting due to the spiralling effect of the steam is the primary reason for the enhancement of the HTC value. It is observed that while the HTC in a spiral tube is inversely related to the spiral diameter, it does not exhibit a strong relationship with the spiral pitch. Moreover, three existing heat transfer correlations are evaluated under the spiral flow condition and it is observed that none of them can calculate the HTC value accurately in spiral tubes. Using the Buckingham p-theorem, three modified correlations are proposed for the low, moderate and high heat flux regimes, which accurately predict the wall temperature and HTC of supercritical steam in spiral tubes in all the heat flux regimes. The correlations have an error band of less than +/-20%.