The higher-dimensional integrable equation induced by the 2+1-dimensional motion of curves in four-dimensional centro-affine geometry is discussed. The curves motion is obtained by adding an extra space variable y to the 1+1-dimensional curves motion in four-dimensional centro-affine geometry

which is equivalent to the surface motion in four-dimensional centro-affine geometry. It is shown that the 2+1-dimensional breaking soliton equation arises from such motion in four-dimensional centro-affine geometry.The result not only extends the existing curve motion in three-dimensional centro-affine geometry to four-dimensional centro-affine geometry

but also enriches geometric explanation of the 2+1-dimensional breaking soliton equation.