The mass limit of neutron star has still remained a mystery. The existing Tolman-Oppenheimer-Volkoff (TOV) equation for calculating the limit always gives different values, by introducing different assumptions and having been predicted like 0.7 Mo, 3.2 Mo, 3.6 Mo, where Mo = 1.98 × 1030 Kg. There is a need of some better technique to adopt other than TOV relation to seek out the value. In this paper, a new relation between the mass of the collapsing star and its average density ρ′ has been derived and used to calculate the limit of neutron star. The conditions in radii between Schwarz Child’s radius and the actual radius of the collapsing star have been introduced to calculate the mass of star above which it will transform into a black hole and below it to a neutron star. A new constant, JN = 8.53707554 × 1039 N-3/2s-3Kg3 has been proposed with which if we introduce the average density of the collapsing neutron star, its mass limit can be calculated very easily. By putting the most possible mass density, which is the minimum required density for a collapsing star to transform into the black hole, it has been found that the mass limit of neutron star is quite higher than it has been assumed. The definition for black hole has also been re-defined on the basis of said radii conditions.