The coordinate sequences of a primitive σ-LFSR sequence over GF(2^k) are m-sequences with the same minimal polynomial over GF(2), thus a primitive σ-LFSR sequence over GF(2^k) can be constructed by m-sequences over GF(2) if its interval vector is known. This paper studies the calculation of interval vectors of a class of primitive σ-LFSR sequences—Z primitive σ-LFSR sequences and presents an improved method to calculate the interval vectors of Z primitive σ-LFSR sequences in order n over GF(2^k), which uses the interval vectors of Z primitive σ-LFSR sequences of order 1 to calculate that of Z primitive σ-LFSR sequences in order n over GF(2^k). In addition, it is more effective than other existing methods. More importantly, the new method can also be applied to the calculation of interval vectors of m-sequences over GF(2^k). The enumeration formula of Z primitive σ-LFSR sequences of order n over GF(2^k) is also presented, which shows that the number of Z primitive σ-LFSR sequences of order n is much larger than the number of m-sequences of order n over GF(2^k).