The size-dependent structural and magnetic properties of nano and bulk samples of 40 mol% Ba2+-doped LaMnO3 (i.e., La0.6Ba0.4MnO3) manganite have been investigated in detail. The Rietveld refinement of X-ray diffraction data confirms that nano and bulk La0.6Ba0.4MnO3 manganites crystallize into ideal cubic perovskite structure with Pm3¯m space group. The refined unit cell parameters decrease with increasing calcinations temperature or particle size. The temperature dependent magnetization measurements reveal that both the bulk and nano samples exhibit paramagnetic (PM) to ferromagnetic (FM) phase transition at Curie temperature (TC). A distinct bifurcation between magnetization curves under zero-field cooled (MZFC) and field-cooled (MFC) measurements reveals the possible existence of frustrated magnetic ordering or spin glass clusters. For nano sample, a sharp downward deviation in inverse susceptibility from Curie-Weiss law is observed, which indicates the existence of Griffiths Phase. The analysis of the field dependent magnetization M(H) curves measured at 10 K, in terms of saturation moments, reveals that there is a coupling between spin and orbital magnetic moments, in bulk sample of La0.6Ba0.4MnO3 manganite, which can be quenched by reducing particle size of the manganite. According to the Banerjee's criterion, nano sample exhibits first-order magnetic transition and bulk sample shows second-order magnetic transition in the low magnetic field region.