Integrating different kinds of pores into one covalent organic framework (COF) endows it with hierarchical porosity and thus generates a member of a new class of COFs, namely, heteropore COFs. Whereas the construction of COFs with homoporosity has already been well developed, the fabrication of heteropore COFs still faces great challenges. Although two strategies have recently been developed to successfully construct heteropore COFs from noncyclic building blocks, they suffer from the generation of COF isomers, which decreases the predictability and controllability of construction of this type of reticular materials. In this work, this drawback was overcome by a multiple-linking-site strategy that offers precision construction of heteropore COFs containing two kinds of hexagonal pores with different shapes and sizes. This strategy was developed by designing a building block in which double linking sites are introduced at each branch of a C -symmetric skeleton, the most widely used scaffold to construct COFs with homogeneous porosity. This design provides a general way to precisely construct heteropore COFs without formation of isomers. Furthermore, the as-prepared heteropore COFs have hollow-spherical morphology, which has rarely been observed for COFs, and an uncommon staggered AB stacking was observed for the layers of the 2D heteropore COFs.