In this paper we define a modular on the Cesaro sequence space $ces(p)$ and consider it equipped with the Luxemburg norm. We give some relationships between the modular and the Luxemburg norm on this space and show that the space $ces(p)$ has property (H) but it is not rotund (R), where $p=(p_k)$ is a bounded sequence of positive real number with $p_kgeq1$ for all $kinmathbb {N}$.

Keywords: Cesaro sequence space, property (H), geometric properties