The temperature and magnetic field dependences of electrical resistivity ρ(Т, Н) and magnetization m(Т, H) of the semiconductor solid solution (Pb0.4Sn0.6)0.8In0.2Te were studied in the temperature range T = 2 K - 300 K (including the region of the superconducting transition of the compound T ≤ 4 K) and in magnetic fields H ≤ 140 kOe. The critical parameters of superconducting transition were determined: the critical temperature Tc ≈ 4 K and the second critical magnetic field at T → 0 K, Hc2(0) ≈ 27.5 kOe. The magnetic field - magnetization dependences m(H) at T < Tc region exhibit a hysteresis loop associated with the magnetic flux capturing by a polycrystalline superconducting sample. In magnetic fields close to the second critical Hc2(T) at temperatures T < 3 K, an additional maximum of the diamagnetic response on the forward branch and a symmetric paramagnetic maximum on the reverse branch were observed on the m(H) dependences, which we interpret as the peak-effect in magnetization of the superconducting solid solution. In the (Pb0.4Sn0.6)0.8In0.2Te sample, at the temperature Т = 2 K and the peak-effect field Нpeak = 16.5 kOe, the magnetization peak amplitude was ~ 6% of the maximum value of the Meissner response at H ≈ 0 Oe. On the basis of the obtained data the possible nature of the peak-effect in the magnetization of solid solutions (PbzSn1-z)1-хInхTe, at Т < Tc was discussed, influence of the vortex structure dynamics of the superconducting compound, the lead content in the solid solution, the level of In doping and external parameters was considered.