In this paper some inequalities on trace of quaternions matrices are proved.They are some generalizations and improvements of[1]--[4].Let Qman denote the set of all m×n matrices over quaternion field. We have: (1) Suppose A∈Qm×n

B∈Qn×m

then trA A tr B B ≥N(tr(AB). (2)A∈Qn×n

then N(trA )≤ntrA A. (3) A≥0

B≥0

then N(trA B)≤(trB)2. (4) Suppose 0≤A=(aij)∈Qn×n and Ri=sum from j=1 to n (N(aij)

then trA≥max{aij-1 Rj|aij≠0}. (5) Suppose A≥0 and A=(A1 A3 A3 A2)

A1∈Q2×3

then trA1 trA2≥ trA3 A3. (6) Suppose 0≤A∈Qn×n

p∈Qn×k

then trP AP≤trAtr P P.