With the mass distribution theory and natural cover

the paper studied a kind of Hausedorff measure of non-homogeneous Moran sets which satisfy the strong separation condition

and proved the following conclusions: for the non-homogeneous Moran sets E determined by({nk}k≥1

{Φk}k≥1

{mk}k≥1)

its s dimension Hausedorff measure is got by multiplying the sum of s powers of the same level ratio ci

j from 1 to k according to i.The limit is also derived on the condition that k

the times of compression

tends to ∞.