Your code is almost right. You managed to get the values from the byte array and to convert them to dword. Now you only have to put them in the dword array (which is even not defined in your program).
Anyway, here it is (FASM syntax):
; data definitions
Array1 db 2, 4, 6, 8, 10
Array2 rd 5 ; reserve 5 dwords for the second array.
; the code
mov esi, Array1
mov edi, Array2
mov ecx, 5
copy_loop:
movzx eax, byte [esi] ; this instruction assumes the numbers are unsigned.
; if the byte array contains signed numbers use
; "movsx"
mov [edi], eax ; store to the dword array
inc esi
add edi, 4 ; <-- notice, the next cell is 4 bytes ahead!
loop copy_loop ; the human-friendly labels will not affect the
; speed of the program.