The invention relates to polyester fibres and a preparation method thereof. The raw material of the polyester fibres is modified polyester which consists of a terephthalic acid chain segment, an ethylene glycol chain segment and a branched chain-containing dihydric alcohol chain segment. The preparation method of the polyester fibres comprises the following steps: performing esterification reaction on terephthalic acid and branched chain-containing dihydric alcohol under the catalysis of concentrated sulphuric acid to obtain terephthalic acid dihydric alcohol ester; then, preparing the terephthalic acid and the ethylene glycol into slurry, and performing the esterification reaction on the slurry to obtain the terephthalic acid ethylene glycol ester; finally, stirring and mixing the terephthalic acid dihydric alcohol ester and the terephthalic acid ethylene glycol ester, and performing condensation polymerization in a low vacuum stage and a high vacuum stage under the action of a catalyst and a stabilizing agent to obtain modified polyester; metering, extruding, cooling, oiling, stretching, heat-setting and winding the polyester to prepare the polyester fibres. The increasing amplitude of the spatial gaps of the polyester fibres is much higher than that of branched chain-free polyester fibres at the same temperature, which is beneficial to the degree of micro particles, such as a dye, that enter the polyester; the dyeing rate is improved.