  Uncertainty relation lies at the heart of quantum mechanics, characterizing
the incompatibility of non-commuting observables in the preparation of quantum
states. An important question is how to improve the lower bound of uncertainty
relation. Here we present a variance-based sum uncertainty relation for $N$
incompatible observables stronger than the simple generalization of the
uncertainty relation for two observables derived by Maccone and Pati [Phys.
Rev. Lett. {\bf113}, 260401 (2014)]. Further comparisons of our uncertainty
relation with other related ones for spin-$\frac{1}{2}$ and spin-$1$ particles
indicate that the obtained uncertainty relation gives a better lower bound.
