The main aim of the present article to introduce a generalization of Fibonacci sequence which is similar to k-Pell, k-Pell-Lucas, Modified k-Pell sequences and known as Fibonacci-Like sequence. After that we obtain some fundamental properties of Fibonacci-Like sequence such as Binet formulae of Fibonacci-Like sequence, binomial transform of the Fibonacci-Like sequence and some other properties of Fibonacci-Like sequence with indexes in an arithmetic sequence. In addition to this we obtain some relations among k-Pell, k-Pell-Lucas, Modified k-Pell and Fibonacci-Like sequences and the most worth noticing cause of the present paper is we present determinantal identities involving k-Pell, k-Pell-Lucas, Modified k-Pell and Fibonacci-Like sequences.