In a rice–wheat rotation system, biochar (BC) applied in different crop seasons undergoes contrast property changes in the soil. However, it is unclear how aged BC affects the production and quality of wheat and the nutrent status in a soil profile. In the present soil column experiment, the effects of no nitrogen (N) fertilizer and BC addition (control), N fertilizer (N420) and BC (5 t ha−1) applied at rice [N420 + BC(R)], or wheat [N420 + BC(W)] seasons at a same rate of N fertilizer (420 kg ha−1 yr−1) on yield and quality of wheat as well as the nutrient contents of soil profiles (0–5, 5–10, 10–20, 20–30, 30–40, and 40–50 cm) were observed. The results showed that N420 + BC(W) significantly reduced NH4+-N content in 5–10 and 10–20 cm soils by 62.1% and 36.2%, respectively, compared with N420. In addition, N420 + BC(W) significantly reduced NO3−-N contents by 17.8% and 40.4% in 0–5 and 20–30 cm profiles, respectively, but N420 + BC(R) slightly increased them. The BC applied in wheat season significantly increased the 0–5 and 40–50 cm soil total N contents (24.0% and 48.1%), and enhanced the 30–40 and 40–50 cm soil-available phosphorus contents (48.2 and 35.75%) as well as improved the 10–20 and 20–30 cm soil-available potassium content (38.1% and 57.5%). Overall, our results suggest that N420 + BC(W) had stronger improving effects on soil fertility than N420 + BC(R). Compared to N420, there was a significant 5.9% increase in wheat grain yield, but no change in total amino acids in wheat kernels in N420 + BC(W). Considering the responses of soil profile nutrient contents as well as wheat yield and quality to BC application in different crop seasons, it is more appropriate to apply BC in wheat season. Our results could provide a scientific basis for the ideal time to amend BC into the rice–wheat rotation system, in order to achieve more benefits of BC on crop production and soil fertility.