Heat transfer enhancement is an important thermal–hydraulic phenomenon in heat exchangers. Previous investigations mostly focused on unidirectional heat transfer enhancement inside the tube. In order to realize the bidirectional heat transfer enhancement inside and outside the tube, an enhanced tube with ellipsoidal dimples and protrusions is proposed. Through comparison among three computational conditions, the non-conjugate and periodic condition is adopted in this paper. Flow characteristics and heat transfer performance of the enhanced tube are investigated by numerical method. The distributions of temperature and flow fields are carried out to illustrate the heat transfer enhancement mechanisms. The Nusselt number, friction coefficient, and performance evaluation criteria (PEC) are presented to reveal thermal–hydraulic performance. Moreover, the effects of the geometric parameters such as dimple depth, dimple pitch, dimples/protrusions numbers in the circumference, and arrangement mode on thermal–hydraulic characteristics are investigated. The results show that the structure of dimples and protrusions induces intensive impingement and interrupts the boundary layers, improving the heat transfer for the internal and external flow, respectively. Besides, the Nu increases with depth and dimples/protrusions numbers in the circumference and decreases with the pitch in most cases. The overall heat transfer performance of staggered arrangement is better than that of aligned arrangement. For the present parameter conditions, when D = 2 mm, P = 25 mm, n = 6, and Re = 5000, the largest PEC of 1.40 and 1.42 occurs for the internal and external flow, respectively.