Summary: Mutually unbiased bases (MUB) and symmetric informationally complete positive operator-valued measure (SIC-POVM) are both important objects in quantum information theory. While people do not know if there exists a complete MUB for non-prime-power dimension, several versions of approximately MUB have been considered by relaxed the inner product condition. So far there are only finite number of \(K\) such that SIC-POVMs in \(\mathbb{C}^k\) have been found. As in the MUB case, several versions of approximately SIC-POVM have been considered by relaxed the inner product condition. In this paper, we use the definitions of approximate MUB and SIC-POVM given by Klappenecker et al. For prime power \(q\), we present simple constructions of \(q\) approximately MUB (AMUB) for dimension \(q-1,\ q+1\) AMUB for dimension \(q-1\), which shows that the number of orthonormal bases of an AMUB in \(\mathbb{C}^k\) can be more than \(K+1\), and \(q\) AMUB for dimension \(q+1\) by Gauss and Jacobi sums. We also present a construction of approximately SIC-POVM (ASIC-POVM) in dimension \(q-1\) by Gauss sum.