This paper introduces a standard logistic L-moment-based system of distributions. The proposed system is an analog to the standard normal conventional moment-based Tukey g-h, g, h, and h-h system of distributions. The system also consists of four classes of distributions and is referred to as (i) asymmetric γ-κ, (ii) log-logistic γ, (iii) symmetric κ, and (iv) asymmetric κL-κR. The system can be used in a variety of settings such as simulation or modeling events—most notably when heavytailed distributions are of interest. A procedure is also described for simulating γ-κ, γ, κ, and κL-κR distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that estimates of L-skew, L-kurtosis, and L-correlation associated with the γ-κ, γ, κ, and κL-κR distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias and relative standard error.