A transmission shaft assembly includes a carbon-fiber tube having two ends, and each end has protrusions and recesses which are located alternatively to the protrusions. Two connectors each have an outer tubular portion and an inner tubular portion extending axially therefrom. Multiple first engaging portions and multiple second engaging portions are located between the outer tubular portion and the inner tubular portion of each of the connectors. The two connectors are respectively connected to the two ends of the carbon-fiber tube. The first engaging portions are engaged with the recesses, and the second engaging portions are engaged with the protrusions. Adhesive is applied between the connectors and the carbon-fiber tube.