It may be used DiagrammeR package to do simple and quick neural network plot.
Plotting neural network that consists of Input layer (I1, I2 and I3), one hidden layer (H1, H2 and H3) and one ouptput variable (O1) can be done as follows.
library(DiagrammeR)
grViz("digraph G1 {
graph [layout=neato overlap = true]
I0 [pos='1,3.25!' shape=plaintext label='input layer' fontsize=20]
I1 [pos='1,2.5!' style=radial fillcolor='gray;0.5:blue' width=.8 height=.8]
I2 [pos='1,1!' style=radial fillcolor='gray;0.5:blue' width=.8 height=.8]
I3 [pos='1,-0.5!' style=radial fillcolor='gray;0.5:blue' width=.8 height=.8]
I7 [pos='0,2.5!' shape=plaintext label='input 1']
I8 [pos='0,1!' shape=plaintext label='input 2']
I9 [pos='0,-0.5!' shape=plaintext label='input 3']
H0 [pos='3,3.25!' shape=plaintext label='hidden layer 1' fontsize=20]
H1 [pos='3,2.5!' style=radial fillcolor='gray;0.5:red' width=.8 height=.8]
H2 [pos='3,1!' style=radial fillcolor='gray;0.5:red' width=.8 height=.8]
H3 [pos='3,-0.5!' style=radial fillcolor='gray;0.5:red' width=.8 height=.8]
O0 [pos='5,1.75!' shape=plaintext label='output layer' fontsize=20]
O1 [pos='5,1!' style=radial fillcolor='gray;0.5:green' width=.8 height=.8]
O7 [pos='6,1!' shape=plaintext label='output']
I7 -> I1
I8 -> I2
I9 -> I3
I1 -> {H1 H2 H3}
I2 -> {H1 H2 H3}
I3 -> {H1 H2 H3}
{H1 H2 H3} -> O1
O1 -> O7
}")