Recently, the niobium (Nb) doped topological insulator Bi 2 Se 3 , in which the finite magnetic moments of the Nb atoms are intercalated in the van der Waals gap between the Bi 2 Se 3 layers, has been shown to exhibit both superconductivity with T c 3 K and topological surface states. Here we report on muon spin rotation experiments probing the temperature and field dependence of effective magnetic penetration depth λ eff (T) in the layered topological superconductor candidate Nb 0.25 Bi 2 Se 3. The exponential temperature dependence of λ −2 eff (T) at low temperatures suggests a fully gapped superconducting state in the bulk with the superconducting transition temperature T c = 2.9 K and the gap to T c ratio 2 /k B T c = 3.95(19). We also reveal that the ratio T c /λ −2 eff is comparable to those of unconventional superconductors, which hints at an unconventional pairing mechanism. Furthermore, time-reversal symmetry breaking was excluded in the superconducting state with sensitive zero-field μSR experiments. We hope the present results will stimulate theoretical investigations to obtain a microscopic understanding of the relation between superconductivity and the topologically nontrivial electronic structure of Nb 0.25 Bi 2 Se 3 .