AbstractThe recently discovered kagome superconductor CsV₃Sb₅ (T_c ≃ 2.5 K) has been found to host charge order as well as a non-trivial band topology, encompassing multiple Dirac points and probable surface states. Such a complex and phenomenologically rich system is, therefore, an ideal playground for observing unusual electronic phases. Here, we report anisotropic superconducting properties of CsV₃Sb₅ by means of transverse-field muon spin rotation (μSR) experiments. The fits of temperature dependences of in-plane and out-of-plane components of the magnetic penetration depth suggest that the superconducting order parameter may have a two-gap (s + s)-wave symmetry. The multiband nature of superconductivity could be further supported by the different temperature dependences of the anisotropic magnetic penetration depth γ_λ(T) and upper critical field ${γ }_{{{{{\rm{B}}}}}_{{{{\rm{c}}}}2}}(T)$ γ B c 2 ( T ) . The relaxation rates obtained from zero field μSR experiments do not show noticeable change across the superconducting transition, indicating that superconductivity does not break time reversal symmetry.