The ultra-low thermal expansion coefficient α makes the Fe-Ni Invar alloys useful in various applications. Their low strength and low Curie temperature Tc are, however, limiting factors. Interestingly, some Fe-based bulk metallic glasses (BMGs), with inherent high strength, exhibit the clear Invar effect. In particular, the (Fe71.2B24Y4.8)96Nb4 BMG has the lowest α among Fe-based BMGs, but it unfortunately also has the lowest Tc. In this work, silicon was added into this alloy with the aim to elevate Tc while maintaining a low α. It was found that when silicon partially substituted boron, Tc did not increase significantly but α did, which is not ideal. On the other hand, when silicon partially substituted yttrium and niobium and especially niobium, Tc increased significantly while α did not, which is close to the ideal scenario. When 3% of niobium was substituted by silicon, Tc reached the maximum value of 296 °C while α remained a low value of 7.4 × 10−6/°C. Comparing to the Fe-Ni Invar alloy, although this BMG has an inferior α, it has much higher Tc (+115 °C) and strength (∼9 times), presenting a potential for application as a new Invar material with moderate (low) thermal expansion, high operating temperature, and high strength.