The normalized cutoff frequencies of the linearly polarized (LP) modes of a graded-index few mode fiber have been calculated as a function of profile shape parameters using a simple numerical method. The effect of refractive-index dip on these cutoff frequencies and on the order of appearance of these modes has been investigated. The presence of dip causes an increase in the cutoff V values of all the modes, and the maximum shift in the cutoff V value is found to be even 20% for some modes. The order of appearance of some modes also gets drastically affected.