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CaSb2 is a topological nodal-line semimetal that becomes superconducting below 1.6 K, providing an ideal platform to investigate the interplay between topologically nontrivial electronic bands and superconductivity. In this work, we investigated the superconducting order parameter of CaSb2 by measuring its magnetic penetration depth change Δλ(T) down to 0.07 K, using a tunneling diode oscillator (TDO) based technique. Well inside the superconducting state, Δλ(T) shows an exponential activated behavior, and provides direct evidence for a nodeless superconducting gap. By analyzing the temperature dependence of the superfluid density and the electronic specific heat, we find both can be consistently described by a two-gap s-wave model, in line with the presence of multiple Fermi surfaces associated with distinct Sb sites in this compound. These results demonstrate fully-gapped superconductivity in CaSb2 and constrain the allowed pairing symmetry.