Order of lewis basic strength
My teacher told me that order of lewis basic strength is inversely proportional to electro negativity. 


I agree with your teacher's guideline. Now, note that this cannot be your sole guideline. Lewis basicity (and acidicty) depend on a number of factors including:


Strength of the corresponding Lewis acid or Lewis base and the strength of the resulting bonds in the Lewis adduct. 
Solvent effects 
Geometry of the interacting species 
Electronegativity 



  Comparing between iodide ion and chloride ion, chloride ion is more electronegative than iodide ion therefore iodide ion should be more basic than chloride ion but the order is reverse that is chloride ion is more basic than iodide ion. 


I think you are confusing Bronsted basicity with Lewis basicity. It is true that in water (a polar, protic solvent) chloride ion is a stronger Bronsted base than iodide ion. 

In terms of Lewis basicity, however, things become a lot more complicated. Iodide ion has the more readily available lone pair electrons for donation since iodide ion is less electronegative than chloride ion. 

On the other hand, the strength of bonds to iodine are generally not as strong as bonds with chloride ion. This is a result of poor orbital overlap between iodide ion - which is a big atom - much bigger than many Lewis acids. 


  I asked my teacher today the same question and he told that since both iodide and chloride ion have delocalize lone pair both iodide and chloride ion have delocalize lone pair in their own vacant orbital therefore the electron donating tendency decreases. here we can't compare using electro negativity. And comparing them since iodide ion has more big size than chloride ion therefore the delocalization tendency is better in iodine therefore chloride ion is better lewis base. Any comments?


I mostly agree; both have electrons in their orbitals but I'm not a fan of the term "delocalization" - that implies that the electrons are spread across multiple nuclei - but in chloride ion and iodide ion there's only one nucleus. 

Again, there are multiple factors to consider - not just electronegativity.