Summary: The omega ratio, a performance measure, is the ratio of the expected upside deviation of return to the expected downside deviation of return from a predetermined threshold described by an investor. It has been exhibited that the omega ratio optimization is equivalent to a linear program under a mild condition and thus easily tractable. But the omega ratio optimization fails to hedge against many other risks involved in portfolio return that may adversely affect the interests of a risk-averse investor. On the other hand, there are widely accepted mean-risk models for portfolio selection that seek to maximize mean return and minimize the associated risk but in general fail to maximize the relative performance ratio around the threshold return. In this paper, we aim to propose a model called ‘extended omega ratio optimization’ that combines the features of the omega ratio optimization model and mean-risk models. The proposed model introduces constraint on a general risk function in the omega ratio optimization model in such a way that the resultant model remains linear and thus tractable. Our empirical experience with real data from S&P BSE sensex index shows that the optimal portfolios from the extended omega ratio optimization model(s) improved over the optimal portfolios from the omega ratio optimization in having less associated risk and over the optimal portfolios from the corresponding mean-risk model(s) in having a high value omega ratio.