The present disclosure relates to a turbo compression system having two or more driving motors provided with a motor-cooling system for efficiently cooling two or more driving motors in the gearless type turbo compressor. An aspect of a turbo compression system having two or more driving motors according to the present disclosure comprises a first, second and third impeller provided separately; two or more driving motor rotating at least one among the first, second and third impeller; and a cooling impeller provided unitarily and simultaneously cooling the two or more driving motor. On the other hand, the turbo compression system having two or more driving motors further may comprise a fan motor rotating the cooling impeller and provided separately from the two or more driving motor.
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