Summary: We study the problem of maximizing a monotone non-submodular function under a \(d\)-knapsack constraint on the integer lattice. We propose three streaming algorithms to approach this problem. We first design a two-pass \(\min \{\alpha (1-\varepsilon)/ 2^{\alpha +1}d,\,1-1/ \alpha_w 2^\alpha-\varepsilon\}\)-approximate algorithm with total memory complexity \(O(\log d \beta^{-1}/\beta \varepsilon)\), and total query complexity for each element \(O(\log \|\mathbf{B} \|_\infty\log d \beta^{-1}/\varepsilon)\). The algorithm relies on a binary search technique to determine the amount of the current elements to be added into the output solution. It also requires to have a good estimate of the optimal value, we use the maximum value of the unit standard vector which can be obtained by reading a round of data to construct a guess set of the optimal value. Then, we modify our algorithm to avoid a repetitive reading of data by dynamically update the maximum value of the unit vector along with the coming elements, and obtain a one-pass streaming algorithm with same approximate ratio. Moreover, we design an improved StreamingKnapsack algorithm to reduce the memory complexity to \(O(d/ \varepsilon^2)\).