Penalized maximum likelihood estimation is specified for estimating parameters of a log-logistic distribution for complete-data situations. This approach addresses the issues of Maximum Likelihood Estimation, wherein Maximum Likelihood Estimation is often unstable when sample sizes are small, and fails with heavy-tailed or asymmetric data. By adding a ridge penalty to the log-likelihood, we derive new score equations, which are solved numerically. The performance is measured for a variety of shape and scale parameters and sample sizes, with bias and Mean Squared Error as the two main measures. The simulation experiment results indicate Penalized maximum likelihood estimation consistently achieves lower bias and Mean Square Error with small sample sizes and particularly strong improvements under skewed or heavy-tailed data. With larger sample size, the differences between Maximum Likelihood Estimation and Penalized maximum likelihood estimation decrease, as we would expect. These results suggest that Penalized maximum likelihood estimation is a viable estimation method using the log-logistic distribution, especially with small or limited datasets.