Every term in the Fibonacci Sequence can be determined recursively with the help of initial values F0 = 0, F1 = 1. Similar is the case with Lucas Sequence. In this paper, we study Generalized Fibonacci-Like sequence {Dn} defined by the recurrence relation Dn = Dn-1 + Dn-2, for all n  2 with D0 = 2 and D1 = 1+m, m being a fixed positive integer. The associated initial conditions are the sum of m times the initial conditions of Fibonacci sequence and the initial conditions of Lucas sequence respectively. We shall define Binet's formula and generating function of Generalized Fibonacci-Like sequence. Mainly, Induction method 236 Sanjay Harne, Bijendra Singh and Shubhraj Pal and Binet's formula will be used to establish properties of Generalized Fibonacci-Like sequence. Mathematics Subject classification: 11B39, 11B37, 11B99