This paper presents a stochastic bi-objective model for a single-allocation hub covering problem (HCP) with the variable capacity and uncertainty parameters. Locating hubs can influence the performance of hub and spoke networks, as a strategic decision. The presented model optimizes two objectives minimizing the total transportation cost and the maximum transportation time from an origin to a destination simultaneously. Then, due to the NP-hardness of the multi-objective chance-constrained HCP, the presented model is solved by a well-known metaheuristic algorithm, namely multi-objective invasive weed optimization. Additionally, the associated results are compared with a well-known multi-objective evolutionary algorithm, namely non-dominated sorting genetic algorithm. Furthermore, the computational results of the foregoing algorithms are reported in terms four well-known metrics, namely quality, spacing, diversification, and mean ideal distance. Finally, the conclusion is reported.Nowadays, transportation and communication networks are of a vital role in modern societies. Thus, optimization of the network design for managing better the traffics and decreasing transport time and cost in acceptable service quality is more important. In this paper, we optimize a network structure for achieving two objectives, namely minimizing the total transport cost and maximum transport time in each allocation when a demand is uncertain. Because of the complexity of the problem, we propose a meta-heuristic algorithm that hss inspired the behavior of invasive weed colonization.