Carbon nanotubes are considered short fibers, and polymer composites with nanotube fillers are always analogues of random, short fiber composites. The real structural carbon fiber composites, on the other hand, always contain carbon fiber reinforcements where fibers run continuously through the composite matrix. With the recent optimization in aligned nanotube growth, samples of nanotubes in macroscopic lengths have become available, and this allows the creation of composites that are similar to the continuous fiber composites with individual nanotubes running continuously through the composite body. In this study, we fabricated such polymer composites with continuous nanotube reinforcements and measured the coefficient of thermal expansion (CTE) of the composites, both in the parallel (longitudinal) and in the normal (transverse) direction to the nanotube axis, respectively. It was experimentally observed the composites have anisotropic thermal expansion property that is attributed to nanotube fillers. Also we suggest a new method on obtaining the CTE values of the carbon nanotubes, which there are difficulties in handling for experiments. Micromechanics models are the equations for predicting the properties of continuous fiber-reinforced composites, consisting of the corresponding properties of the constituent materials as the parameters. Through the CTE measurement experiments of the composites, we can get the longitudinal CTE and transverse CTE of the composites. In addition, by consulting literature and conducting experiments we can get the other values of each parameter except CTEs of the carbon nanotubes. Finally, we can calculate the longitudinal and transverse CTEs of carbon nanotubes in reverse.