Layered indium selenide (InSe) has emerged as a promising two-dimensional semiconductor due to its high electron mobility and direct optical bandgap in the few-layer limit. As InSe is integrated into high-performance electronic and optoelectronic systems, thermal management will become critical, thus motivating detailed characterization of intrinsic thermal properties. Here, we report the room-temperature thermal conductivity of exfoliated crystals of InSe along the through-plane and in-plane directions using conventional and beam offset time-domain thermoreflectance (TDTR), respectively. InSe crystals with varying thicknesses were prepared by mechanical exfoliation onto Si(100) wafers followed by immediate encapsulation with a 3-nm-thick AlOx passivation layer to prevent ambient degradation prior to coating with metal films for TDTR measurements. The measured thermal conductivity in the in-plane direction, Λin ≈ 8.5 ± 2 W/m K, is an order of magnitude higher than that in the through-plane direction, Λthrough ≈ 0.76±0.15 W/m K, which implies a high thermal anisotropy ≈11 ± 3. These relatively high anisotropy and low thermal conductivity compared to other layered semiconductors imply that InSe will require unique thermal management considerations when implemented in electronic, optoelectronic, and thermoelectric applications.