diff --git a/src/univariate/continuous/laplace.jl b/src/univariate/continuous/laplace.jl
index ebd3945ea8..3d3a43154d 100644
--- a/src/univariate/continuous/laplace.jl
+++ b/src/univariate/continuous/laplace.jl
@@ -121,3 +121,27 @@ function fit_mle(::Type{<:Laplace}, x::AbstractArray{<:Real})
     xc .= abs.(x .- m)
     return Laplace(m, mean(xc))
 end
+
+function fit_mle(::Type{<:Laplace}, x::AbstractArray{T}, w::AbstractArray{T}) where {T <: Real}
+    sp = sortperm(x)
+    n = length(x)
+    sw = sum(w)
+    highsum = sw
+    lowsum = zero(T)
+    idx = 0
+    for i = 1:n
+        lowsum += w[sp[i]]
+        highsum -= w[sp[i]]
+        if lowsum >= highsum
+            idx = sp[i]
+            break
+        end
+    end
+    μ = x[idx]
+    θ = zero(T)
+    for i = 1:length(x)
+        θ += w[i] * abs(x[i] - μ)
+    end
+    θ /= sw
+    return Laplace(μ, θ)
+end
diff --git a/test/fit.jl b/test/fit.jl
index 4cf299c6aa..5652c1be25 100644
--- a/test/fit.jl
+++ b/test/fit.jl
@@ -362,6 +362,15 @@ end
     end
 end
 
+@testset "Testing fit for Laplace with weights" begin
+    for func in funcs, dist in (Laplace, Laplace{Float64})
+        d = fit(dist, func[2](dist(5.0, 3.0), N + 1), ones(Float64, N+1))
+        @test isa(d, dist)
+        @test isapprox(location(d), 5.0, atol=0.01)
+        @test isapprox(scale(d)   , 3.0, atol=0.01)
+    end
+end
+
 @testset "Testing fit for Pareto" begin
     for func in funcs, dist in (Pareto, Pareto{Float64})
         x = func[2](dist(3., 7.), N)