Financial risk has a heavy-tailed profile, so a new risk measure called tail value-at-risk (TVaR)-based expectile was developed to capture extreme risks better than traditional methods. The properties of TVaR-based expectiles were studied, showing they are well-defined and coherent. For extreme risks, the TVaR-based expectile was analyzed with respect to quantiles. A closed-form worst-case TVaR-based expectile was derived based on moment information, simplifying portfolio selection problems. Numerical results demonstrated the effectiveness of the new risk measure compared to traditional ones.