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We generalize the maximal diameter sphere theorem due to Toponogov by meansof the radial curvature. As a corollary to our main theorem, we prove that fora complete connected Riemannian $n$-manifold $M$ having radial sectionalcurvature at a point bounded from below by the radial curvature function of anellipsoid of prolate type, the diameter of $M$ does not exceed the diameter ofthe ellipsoid, and if the diameter of $M$ equals that of the ellipsoid, then$M$ is isometric to the $n$-dimensional ellipsoid of revolution.

Maximal diameter sphere theorem for manifolds with nonconstant radial curvature