I have 3 IV's and they are significantly correlated with DV, but when I run regression one of the IV's Beta value turns out to be insignificant. What might be the reason of this?
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When you have multiple independent variables in a regression then the regression coefficient for each of them controls for the others. That is, with IVs X1, X2 and X3, the coefficient for X1 is looking at the relationship between Y and X1 while holding X2 and X3 constant.

Peter Flom
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You mean if there is a mediation effect between two or more IV's, such an outcome is normal? – Jan 05 '16 at 11:33
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yes. This sort of thing is normal in non-experimental designs where the IVs are related to each other – Peter Flom Jan 05 '16 at 21:19