Lagged Fibonacci Generators (LFG) are used as a building block of key-stream generator in stream cipher cryptography. In this note, we have used the self-shrinking concept in LFG and given an upper bound 2n+m/8 for the self-shrinking LFG, where n is the number of stage and m is the word size of the LFG. We have also shown that the bound is attained by all the LFGs of degree n < 28, result supported by experiments.