We have investigated the effects of Ti-doping at the Mn-site of La0.6Ba0.4Mn1–xTixO3–δ (0.02 ≤ x ≤ 0.08) manganites produced via an auto-combustion technique on the structural and magnetic behavior. All of the compositions crystallize into a cubic structure with Pm3‾m space group as confirmed using Rietveld analysis of the X-ray diffraction data. Unit cell lattice parameter ‘a’ and volume ‘V’ increase upon increasing the doping concentration, which revealed that the larger Ti-ions substitute the smaller Mn-ions in the lattice. Temperature-dependent magnetization measurements revealed that all of the compositions undergo a paramagnetic to ferromagnetic transition at the Curie-temperature (TC). The TC decreases non-linearly from 309 to 212 K as the concentration of Ti-ions increases from x = 0.02 to 0.08. An abnormal behavior in the experimental effective paramagnetic moment was observed in La0.6Ba0.4Mn1–xTixO3–δ (0.02 ≤ x ≤ 0.08), which increases with the substitution of magnetic Mn-ions by Ti-ions. The experimental paramagnetic moment increases non-linearly from 6.10 to 6.52 μB. The downturn deviation in the inverse susceptibility from Curie–Weiss law for the sample with x = 0.08 revealed the appearance of a Griffiths phase. The singularity of the dc inverse susceptibility in the Griffiths phase region provided the numerical values of the Griffiths temperature (TG), critical temperature for random ferromagnet (TCR), and critical exponent (λGP) to be 310 K, 247.7 K, and 0.95(1), respectively. In the low temperature region, the larger value of the experimental saturation moment compared to the corresponding theoretical values observed for the La0.6Ba0.4Mn1–xTixO3–δ manganites indicates the possibility of spin-orbit coupling.