The evaluation of disconnected quark loops are often required in the lattice QCD calculations and very computer time consuming. To compute these diagrams, stochastic noise methods are generally used. However, stochastic estimation has large error in the calculations of the pseudoscalar disconnected diagrams. We use a symmetric multi-probing method (SMP) to estimate these disconnected quark loops. We compare the SMP method to the $Z(2)$ noise method for computing the pseudoscalar disconnected quark loops on quenched lattice QCD ensemble with lattice volume $12^{3}\times24$ at lattice spacing $a\approx0.1\text{fm}$. It is found that the SMP method is very suitable for the calculation of the pseudoscalar disconnected quark loops.