Under fidic, if boq quantity is more than the drawing quantity, which one the contractor is supposed to complete within the contract period?

The BOQ Quantity. Because the Contract between the parties was based on the BOQ Quantity, and thereafter the Contractor Planned his activties according to the qunatities sepcified in the BOQ. The Contractor under the condition of the contract is obligated to complete the works, along with any varatiaons. 

It is assumed that the question refers to either FIDIC Red Book or FIDIC Red Book. Both of these forms of contract are intended for re-measured contracts, in which case the Contractor is obliged to execute as per the drawings and specifications and the quantities of which will be re-measured for payment purpose.

However, due to the nature of the question, it seems that aforesaid forms of contract are used in a context of lump sum payment. In that case, the Contractor is obliged to execute the work as per the Drawings and Specifications since those are the documents which define the scope (unless BOQ quantities are defined in the Contract to be binding). The purpose of the BOQ is to have breakdown of prices for interim payments and to be used as a reference for pricing/evaluating variations.