What are you trying to alkylate with?

Alkyl Bromide... this reaction is easily proceed with sodium methoxide...but want to replace sodium methoxide with NaOH

Any reason you only want to use NaOH? In my experience NaH in DMSO would be best. You can download my DIC thesis from Research Gate which as some experimental procedures for mono and di alkylated malonates. If NaH is too expensive or hazardous you can use NaOMe (just be careful not to use too big an excess or you will get some transesterification). Hope this helps.

Use ethanol as a solvent, add powdered NaOH. Should still work fine. Water is unlikely to interfere.

I agree with E. B. J. Harris, but you have to try it... pKa of malonate is about 13, so it may work... However, I have no experience with this so far.

I think the pKa is probably ok, NaOH will be strong enough but I'm not sure that ethanol is the best choice of solvent. Depending on the alkyl bromide in question, putting the second alkyl group on might be a bit slow and DMSO will speed things along nicely and can also run at higher temperatures if needed. It really depends on substrates. NaOH in EtOH might work fine and is cheap, safe (but flammable) and convenient. But if reaction is slow or low yielding, head for the DMSO :)

Yes, you are right... EtOH is strong enought to protonate an anion of monoalkyl-malonate, so for dialkyl derivative it is better to use an aprotic inert solvent... I was thinking only about a base...:) 

I have a doubt, NaOH/KOH act as nucleophile and not as base in the presence of alcohol. So is alkylation possible with this combination, EtOH-NaOH?

Ethanol and NaOH works well for ethyl malonate. Use methanol, instead, is you have methyl malonate. Always the same solvent as the ester used.

The ester CO CAN AND WILL be attacked by the nucleophilic alcoholate, so if you use a methyl malonate in ethanol, a transesterification will be produced, and you'll end up with a mixture of esters, depending on conditions used.

Thanks every body i have drawn following conclusion from your comments.

Note : "Transesterification is not a problem"

experiment options:

1) NaOH/ KOH with Ethanol or Methanol  

2) NaOH in DMSO or in aprotic solvent.

Will share that whose idea works..

A catalytic amount of a tetrabutylammonium salt might help move things along.