We study a Gross-Pitaevskii equation with a trap potential under the unit mass constraint, which is used to describe Bose-Einstein condensates with attractive interaction. First, we provide some necessary conditions for the existence of a solution concentrating at a curve. Next, under stationary and non-degeneracy assumptions on the curve with respect to an auxiliary weighted length involving the trap potential, we construct a solution with concentration directed along the curve, provided that the parameter $-\lambda \to +\infty$. Our result improves upon very recent results by Q. Guo, S. Tian and Y. Zhou in Calc. Var. Partial Differential Equations (Vol. 61, 2022, no. 2), which relied heavily on the radial symmetry assumption of the trap potential. This is a joint work with Lipeng Duan and Suting Wei.