You need to edit your data to be only those greater than zero (negative and zero values will not plot on a loglog plot anyway, so you lose nothing by eliminating them), then a simple patch call works:
fidi = fopen('Mainul Hoque limit.txt','r');
limitc = textscan(fidi, '%f%f%f%f', 'CollectOutput',1);
limit = limitc{:};
a=limit(:,1);
upper=limit(:,2);
lower=limit(:,3);
avg=limit(:,4);
idx = upper>0 & lower>0 & avg>0; % Eliminate Negative & Zero Data
figure(1)
patch([a(idx)' fliplr(a(idx)')], [lower(idx)' fliplr(upper(idx)')], [0.8 0.8 0.8])
hold on
plot(a(idx),avg(idx), a(idx),upper(idx), a(idx),lower(idx))
hold off
set(gca, 'XScale', 'log', 'YScale','log')
I used a light gray triple [0.8 0.8 0.8] for the fill colour. Use whatever colour works for you.
