Let \(I=[0,1]\) and \(f: I\to I\) be a continuous map. For any finite open cover of \(I\), denote \(\mathcal{N}(\vee_{i=0}^{n-1}f^{-i}\alpha)\) the smallest cardinality of a subcover chosen from the open cover \(\vee_{i=0}^{n-1}f^{-i}\alpha=\{\cap_{i=0}^{n-1}f^{-i}(A_{j_i}) : A_{j_i}\in\alpha\}\), the topological entropy is defined as the non-negative number \[ h(f)=\sup_\alpha\lim_{n\to\infty}\frac{1}{n}\log\mathcal{N}(\vee_{i=0}^{n-1}f^{-i}\alpha). \] On the other hand, with the time series analysis, let \((x_n)^\infty_{n=0}\) be a sequence, and \(\mathcal{A}_n\subset \mathcal{S}_n\) be the subset of permutations with the property that for any \(\pi\in\mathcal{A}_n\), there is \(k\in\mathbb{N}\) such that \(x_{k+\pi(1)}<x_{k+\pi(2)}<\cdots<x_{k+\pi(n)}\). The permutation entropy of the sequence is defined as \[ h^*((x_n)^\infty_{n=0})=\mathop{\lim\sup}_{n\to\infty}\frac{1}{n}\log \sharp\mathcal{A}_n. \] The main result of the paper is that if \(f:I\to I\) is continuous and monotone, then for any \(y\in I\), \[ h^*(Orb(y, f))\leq h(f)=sup_{x\in I}h^*(Orb(x, f)). \] The paper also provides some numerical estimations of the topological entropy. One approach is to choose some \(x_0, x_1, \cdots, x_n\in I\) and estimate the entropy \(h(f)\) from \(\max_{0\leq i\leq n}h^*(Orb(x_i, f))\). The sequence \(S(x, n_0)=(f^n(x))^{n_0}_{n=0}\subset Orb(x, f)\) is selected to numerically compute \(h^*(Orb(x_i, f))\).