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I use a non-linear model to compare welfare under different monetary policies. After I check the IRF in first order approximation, I simulate the model in the second order approximation. I use the methods introduced in this forum to add a welfare function. But the simulation results show the welfare under floating exchange rate is smaller than that under fixed exchange rate. It is totally counter-intuition. Does anyone come across the similar problems? Thank you!

You need to understand the tradeoffs in your model to find out whether this makes intuitive sense. It could in principle happen that flexible exchange rates decrease welfare (the exchange rate is one price, but it is influences both the goods market and the asset market; With one instrument, you cannot achieve two goals), but this sounds rather pathological.
Most probably, there is still some mistake.