In this paper, we introduce weakly 1-absorbing primary submodules of modules over commutative rings. Let R" role="presentation" >R be a commutative ring with a nonzero identity and M" role="presentation" >M be a nonzero unital module. A proper submodule N" role="presentation" >N of M" role="presentation" >M is said to be a weakly 1-absorbing primary submodule if whenever 0≠abm∈N" role="presentation" >0≠abm∈N for some nonunit elements a,b∈R" role="presentation" >a,b∈R and m∈M," role="presentation" >m∈M, then ab∈(N:M)" role="presentation" >ab∈(N:M) or m∈M" role="presentation" >m∈M-rad(N)," role="presentation" >rad(N), where M" role="presentation" >M-rad(N)" role="presentation" >rad(N) is the prime radical of N." role="presentation" >N. Many properties and characterizations of weakly 1-absorbing primary submodules are given. We also give the relations between weakly 1-absorbing primary submodules and other classical submodules such as weakly prime, weakly primary, weakly 2-absorbing primary submodules. Also, we use them to characterize simple modules.