In this study, the extruded Mg–Zn–Mn–Ce–Ca alloy tube with a weak basal fiber texture, i.e. the {0001} plane is distributed along the TD with 0°∼30° deflection towards ED, was fabricated. The alloy tube exhibits a low mechanical anisotropy in the tensile process at room temperature. To clarify the relationship between the weak texture and the low mechanical anisotropy, the microstructure and deformation mechanism of the alloy tube in the tensile process along the ED, 45ED and TD were studied. The results revealed that during yielding, the deformation in ED sample was governed by predominant prismatic slip, and a portion of additional basal slip and lowest pyramidal <c+a> slip, while predominant basal slip and accompanied by a high fraction of prismatic slip and lowest pyramidal <c+a> slip for both 45ED and TD samples. These relatively high additional slips result from the weak texture, which attenuates the deformation differences among the three samples. After yielding, the three samples underwent similar prismatic slip transition and twin nucleation quantity. Additionally, the {0001} plane displayed to converge towards the RD after tensile fracture, which may be related to the twins and intragranular slip. Especially for 45ED and TD samples, relatively high basal slip may cause their {0001} plane to tend to be parallel to the loading direction. In summary, the similar deformation mechanisms governed by weak texture along the three directions resulted in the low mechanical anisotropic of the alloy tube.