Abstract For the critical one-dimensional nonlinear Schrödinger equation, we construct blow-up solutions that concentrate a soliton at the origin at the conformal blow-up rate, with a nonflat blow-up profile. More precisely, we obtain a blow-up profile that equals ∣ ∣ x ∣ ∣ + i κ x 2 near the origin, where κ is a universal real constant. Such profile differs from the flat profiles obtained in the same context by Bourgain and Wang in 1997.