A novel miniaturised quad-band printed Vivaldi antenna is proposed for millimetre-wave applications. It can be seen as a two-arm antenna where the antenna arms bound the tapered Vivaldi slot. The antenna arms are printed on the opposite sides of a flexible millimetre-wave substrate. Three periodic structures are added to the antenna geometry and printed in the area surrounding the radiating slot structure to improve the impedance matching over the antenna's four operational frequency bands and enhance the gain. These periodic structures are parasitic ring array loaded to the antenna arms, ring-array reflector inserted between the antenna arms and the ground plane, and metamaterial director printed in front of the antenna arms. A prototype of the proposed antenna is fabricated for experimental assessment of the antenna performance. The experimental measurements show good agreement with the simulation results. The proposed antenna impedance is matched over the four frequency bands centred at $25$25, $35$35, $45$45, and $55{\rm{ GHz}}$55GHz. The bandwidth of each operational band is about $5{\rm{ GHz}}$5GHz with percent bandwidths of $20\% $20%, $15\% $15%, $11\% $11%, and $9\% $9%, respectively. The corresponding values of the maximum gain are $7.5$7.5, $10.5$10.5, $12$12, and $13{\rm{ dBi}}$13dBi, respectively. The radiation efficiency is maintained above $93\% $93% over the entire frequency band (20-60 GHz).