In practical engineering, the extensive presence of time-variant uncertainty significantly affects structural safety. To efficiently and accurately describe the time-variant uncertainty variables with few samples and insufficient information, a minimum interval radius-based interval process model (MIR-IPM) is proposed. The construction of MIR-IPM involves establishing the corresponding ellipsoid to envelope all measured samples with the minimum interval radius. Thus, it is equivalent to solving a large-scale optimization problem. This paper further uses the coordinate transformation to reduce the dimension of samples, thereby reducing the number of optimization variables and improving the construction efficiency. At last, numerical experiments have verified the efficiency and accuracy of the proposed method in describing the time-variant uncertainty variables with few samples.