Causal interaction between different brain regions has received wide attention recently. Granger causality (GC) is one of the most popular methods to explore causality relationship between different brain regions. New causality (NC) proposed by Hu et. al was shown to be better reveal true causality than GC. In this paper based on scalp EEGs from 6 groups subjects we apply GC and NC methods to study shared intentionality which is an important mental process in cognitive neuroscience and psychology. We are interested in nine regions: F3 (left area of the frontal cortex), Fz (central area of the frontal cortex), F4 (right area of the frontal cortex), C3 (left area of the central cortex), Cz (central area of the central cortex), C4 (right area of the central cortex), P3 (left area of the parietal cortex), Pz (central area of the parietal cortex), P4 (right area of the parietal cortex) which are considered to be optimal locations for observing whether the scalp EEGs can yield information about the timing of episodically synchronized brain activity in higher cognitive function. Our findings show that i) there exists obvious stronger causal influence from F3/Fz/F4/Cz/C4/P3/Pz/P4 to C3 in 8 ∼ 13Hz rhythm than that from C3 to F3/Fz/F4/Cz/C4/P3/Pz/P4 for three states (eyes open+finger movement, eyes wandering+finger movement, and eyes close+finger movement) during shared intentionality. ii) NC method can better reveal real causal influence in 8 ∼ 13Hz rhythm than GC method during three states.