We consider the simplest quartic number fields K m defined by the irreducible quartic polynomials x 4 − mx 3 − 6x 2 + mx + 1, where m runs over the positive rational integers such that the odd part of m 2 + 16 is square free. In this paper, we study the index I(K m) and determine the explicit prime ideal factorization of rational primes in simplest quartic number fields K m. On the other hand, we establish an asymptotic formula for the number of simplest quartic fields with discriminant ≤ x and given index