Abstract: Research on isogeomatric analysis on a complex computational domain is one of the key problems.Normally a complex computational domain is composed by several simple patches with geometric continuity.Thus,it is necessary to discuss the relationship between the convergence of isogeometric analysis and geometric continuity.Solving Laplace-Beltrami equation on a geometrically continuous curve by analysis isogeometric analysis error theory is discussed.Based on this theoretic result,a method for choosing a spline space to ob-tain an optimal convergence rate in isogeometric solving is introduced and the numerical experiments are il-lustrated.Moreover,we validate the spline space,chosen by its approximate property,reaches the optimal convergence rate numerically.The results provide a theoretical basis for isogeometric analysis on complex computational domains.