In this paper, we compare the largest order statistics arising from independent heterogeneous Weibull random variables based on the likelihood ratio order. Let X1,…,Xn$$X_{1},\ldots ,X_{n}$$ be independent Weibull random variables with Xi$$X_{i}$$ having shape parameter 0<α≤1$$0<\alpha \le 1$$ and scale parameter λi$$\lambda _{i}$$, i=1,…,n$$i=1,\ldots ,n$$, and Y1,…,Yn$$Y_{1},\ldots ,Y_{n}$$ be a random sample of size n from a Weibull distribution with shape parameter 0<α≤1$$0<\alpha \le 1$$ and a common scale parameter λ¯=1n∑i=1nλi$$\overline{\lambda }=\frac{1}{n}\sum \nolimits _{i=1}^{n}\lambda _{i}$$, the arithmetic mean of λi′s$$\lambda _{i}^{'}s$$. Let Xn:n$$X_{n:n}$$ and Yn:n$$Y_{n:n}$$ denote the corresponding largest order statistics, respectively. We then prove that Xn:n$$X_{n:n}$$ is stochastically larger than Yn:n$$Y_{n:n}$$ in terms of the likelihood ratio order, and provide numerical examples to illustrate the results established here.