Both Fuzzy set theory and rough set theory are effective tools in dealing with uncertainty problems. However, these theories have their own inherent limitation, which is the inadequacy of the parameterizations tool. Soft set theory is a new mathematical tool in dealing with uncertainties which is free from the above difficulties. Soft set can deal with broader uncertain problems by the combination of them. The present paper aims to further generalize intuitionistic fuzzy soft sets and investigate their application in multiattribute decision making. A new soft computing model called generalized intuitionistic fuzzy soft sets is defined and some related properties are investigated. This new model could give approximate description of concerned objects in an intuitionistic fuzzy environment, together with some additional information on the weights of attributes. We consider the application of generalized intuitionistic fuzzy soft sets in multiattribute decision making. In particular, an effective algorithm to solve such decision making problems is presented and supported by illustrative examples.