An increasing number of two-dimensional (2D) materials have already been achieved experimentally or predicted theoretically, which have potential applications in nano- and opto-electronics. Various applications for electronic devices are closely related to their thermal transport properties. In this work, the strain dependence of phonon transport in monolayer SiC with a perfect planar hexagonal honeycomb structure is investigated by solving the linearized phonon Boltzmann equation. It is found that room-temperature lattice thermal conductivity ($kappa_L$) of monolayer SiC is two orders of magnitude lower than that of graphene. The low $kappa_L$ is due to small group velocities and short phonon lifetimes, which can also be explained by polarized covalent bond due to large charge transfer from Si to C atoms. In considered strain range, it is proved that the SiC monolayer is mechanically and dynamically stable. With increased tensile strain, the $kappa_L$ of SiC monolayer shows an unusual nonmonotonic up-and-down behavior, which is due to the competition between the change of phonon group velocities and phonon lifetimes of low frequency phonon modes. At low strains ($<$8%), the phonon lifetimes enhancement induces the increased $kappa_L$, while at high strains ($>$8%) the reduction of group velocities as well as the decrease of the phonon lifetimes are the major mechanism responsible for decreased $kappa_L$. Our works further enrich studies on phonon transports of 2D materials with a perfect planar hexagonal honeycomb structure, and motivate farther experimental studies.
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