In this paper, we discuss problems that integer part of nonlinear forms with prime variables represent primes infinitely. We prove that under suitable conditions there exist infinitely many primes $p_j,p$ such that $[{\lambda }_1{p}_1^2+{\lambda }_2{p}_2^2+{\lambda }_3{p}_3^k]=p$ and $[{\lambda }_1{p}_1^3+\cdots +{\lambda }_4{p}_4^3+{\lambda }_5{p}_5^k]=p$ with $k\ge 2$ and $k\ge 3$ respectively, which improve the author's earlier results.