In this short paper, we establish an Hélein’s type convergence theorem for conformal immersions from
S
2
\mathbb {S}^{2}
to a general compact Riemannian manifold. As an application, we extend the existence of minimizer of
∫
|
A
|
2
d
μ
\int |A|^{2} d\mu
for immersed 2-spheres in compact 3-manifolds under certain conditions due to E. Kuwert, A. Mondino, and J. Schygulla to higher codimensions.