We report the emergence of superconductivity in Li doped Ba-122 single crystals grown by the Bridgman method. The superconducting transition temperature Tc,onset is around 19 K. The specific heat capacity C/T shows a weak anomaly near Tc. The value of ΔC/γnTc is smaller than the value predicted in BCS theory indicating a multigap nature of the sample. The magnetic measurements show that the lower critical field Hc1(T) exhibits a linear temperature dependence, with a pronounced change of the Hc1(T) curvature around 0.4Tc and Hc1(0) ≈ 430 Oe in the Ba0.6Li0.4Fe2As2 single crystal. Furthermore, temperature dependence of the penetration depth λ(T) follows a power law (~T(n)) below 0.4Tc which predicts possible S±-wave pairing in a Ba0.6Li0.4Fe2As2 superconductor. Over a wide range of temperatures, the Jc(H) exhibits a relation J(c)[proportionality] H(-α) with α = 0.5 ~ 0.6 for H || c and H || ab which indicates random defects in the sample. We found that the temperature dependence of the critical current density Jc(T) can be fitted well with the δl-type pinning model, whose origin is attributed to spatial variations of charge carrier mean free path l. We suggest that the large mismatch in the ionic radius of Ba and Li can affect the irreversible magnetic properties of the Ba0.6Li0.4Fe2As2 single crystal without any structural transition.